Operator Extensions Interpolation Of Functions And Related Topics

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Operator Extensions, Interpolation of Functions and Related Topics

A. Gheondea,D. Timotin,F.H. Vasilescu
Operator Extensions Interpolation of Functions and Related Topics Book PDF

Author : A. Gheondea,D. Timotin,F.H. Vasilescu
Publisher : Birkhäuser
Page : 225 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034885751

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Operator Extensions, Interpolation of Functions and Related Topics by A. Gheondea,D. Timotin,F.H. Vasilescu Pdf

Since 1976 the Institute of Mathematics of the Romanian Academy (formerly the Department of Mathematics of INCREST) and the Faculty of Mathematics (formerly the Faculty of Sciences) of the University ofTimi~oara have organized several Con ferences on Operator Theory. These Conferences were held yearly in Timi~oara (or in Timi~oara and Herculane) and beginning with 1985 they were held in Bucharest (1985,1986), in Timi~oara (1988) and in Predeal (1990). At the beginning, these Conferences answered the need of a part of the Romanian Mathematical Community ofexploring other forms of survival, after the dissolution of the Institute of Mathematics in 1975. Soon, these meetings evolved to International Conferences with a broad participation and where important results in Operator Theory and Operator Algebras and their interplay with Complex Function Theory, Differential Equations, Mathematical Physics, System Theory, etc. were presented. The 14th Conference on Operator Theory was held between June 1st and June 5th 1992, at the University ofTimi~oara. It was partially supported by the Institute of Mathematics of the Romanian Academy and by the Faculty of Mathematics of the University ofTimi~oara. Another important contribution towards covering the costs of this meeting came from The Soros Foundation for an Open Society. Without this generous help the organizing of this event would be impossible. Since 1980, the Proceedings of OT Conferences were published by Birkhauser Verlag in the series Operator Theory: Advances and Applications. The abstracts of the talks were collected in the Conference Report, published by the University of Timi~oara.

Nonselfadjoint Operators and Related Topics

A. Feintuch,I. Gohberg
Nonselfadjoint Operators and Related Topics Book PDF

Author : A. Feintuch,I. Gohberg
Publisher : Birkhäuser
Page : 433 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885225

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Nonselfadjoint Operators and Related Topics by A. Feintuch,I. Gohberg Pdf

Our goal is to find Grabner bases for polynomials in four different sets of expressions: 1 x- , (1 - x)-1 (RESOL) X, 1 x- (1 - xy)-1 (EB) X, , y-1, (1-yx)-1 y, (1_y)-1 (1-x)-1 (preNF) (EB) plus and (1 - xy)1/2 (1 - yx )1/2 (NF) (preNF) plus and Most formulas in the theory of the Nagy-Foias operator model [NF] are polynomials in these expressions where x = T and y = T*. Complicated polynomials can often be simplified by applying "replacement rules". For example, the polynomial (1 - xy)-2 - 2xy(1-xy)-2 + xy2 (1 - xy)-2 -1 simplifies to O. This can be seen by three applications of the replacement rule (1-xy) -1 xy -t (1 - xy)-1 -1 which is true because of the definition of (1-xy)-1. A replacement rule consists of a left hand side (LHS) and a right hand side (RHS). The LHS will always be a monomial. The RHS will be a polynomial whose terms are "simpler" (in a sense to be made precise) than the LHS. An expression is reduced by repeatedly replacing any occurrence of a LHS by the corresponding RHS. The monomials will be well-ordered, so the reduction procedure will terminate after finitely many steps. Our aim is to provide a list of substitution rules for the classes of expressions above. These rules, when implemented on a computer, provide an efficient automatic simplification process. We discuss and define the ordering on monomials later.

J-Contractive Matrix Valued Functions and Related Topics

Damir Z. Arov,Harry Dym
J Contractive Matrix Valued Functions and Related Topics Book PDF

Author : Damir Z. Arov,Harry Dym
Publisher : Cambridge University Press
Page : 576 pages
File Size : 41,7 Mb
Release : 2008-11-06
Category : Mathematics
ISBN : 9780521883009

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J-Contractive Matrix Valued Functions and Related Topics by Damir Z. Arov,Harry Dym Pdf

A comprehensive introduction to the theory of J-contractive and J-inner matrix valued functions with respect to the open upper half-plane and a number of applications of this theory. It will be of particular interest to those with an interest in operator theory and matrix analysis.

Topics in Interpolation Theory

Bernd Fritzsche,Victor Katsnelson,Bernd Kirstein
Topics in Interpolation Theory Book PDF

Author : Bernd Fritzsche,Victor Katsnelson,Bernd Kirstein
Publisher : Birkhäuser
Page : 509 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889445

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Topics in Interpolation Theory by Bernd Fritzsche,Victor Katsnelson,Bernd Kirstein Pdf

About one half of the papers in this volume are based on lectures which were pre sented at a conference at Leipzig University in August 1994, which was dedicated to Vladimir Petrovich Potapov. He would have been eighty years old. These have been supplemented by: (1) Historical material, based on reminiscences of former colleagues, students and associates of V.P. Potapov. (2) Translations of a number of important papers (which serve to clarify the Potapov approach to problems of interpolation and extension, as well as a number of related problems and methods) and are relatively unknown in the West. (3) Two expository papers, which have been especially written for this volume. For purposes of discussion, it is convenient to group the technical papers in this volume into six categories. We will now run through them lightly, first listing the major theme, then in parentheses the authors of the relevant papers, followed by discussion. Some supplementary references are listed at the end; OT72 which appears frequently in this volume, refers to Volume 72 in the series Operator Theory: Advances and Applications. It was dedicated to V.P. Potapov. 1. Multiplicative decompositions (Yu.P. Ginzburg; M.S. Livsic, I.V. Mikhailova; V.I. Smirnov).

Topics In Interpolation Theory

Harry Dym
Topics In Interpolation Theory Book PDF

Author : Harry Dym
Publisher : Springer Science & Business Media
Page : 526 pages
File Size : 41,5 Mb
Release : 1997
Category : Mathematics
ISBN : 3764357231

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Topics In Interpolation Theory by Harry Dym Pdf

Vladimir Petrovich Potapov, as remembered by colleagues, friends and former students.- On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc.- On tangential interpolation in reproducing kernel Hilbert modules and applications.- Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions.- The indefinite metric in the Schur interpolation problem for analytic functions, IV.- Bitangential interpolation for upper triangular operators.- Bitangential interpolation for upper triangular operators when the Pick operator is strictly positive.- Integral representations of a pair of nonnegative operators and interpolation problems in the Stieltjes class.- On recovering a multiplicative integral from its modulus.- On Schur functions and Szegö orthogonal polynomials.- Hilbert spaces of entire functions as a J theory subject.- On transformations of Potapov's fundamental matrix inequality.- An abstract interpolation problem and the extension theory of isometric operators.- On the theory of matrix-valued functions belonging to the Smirnov class.- Integral representation of function of class Ka.- On the theory of entire matrix-functions of exponential type.- Analogs of Nehari and Sarason theorems for character-automorphic functions and some related questions.- The Blaschke-Potapov factorization theorem and the theory of nonselfadjoint operators.- Weyl matrix circles as a tool for uniqueness in the theory of multiplicative representation of J-inner functions.- On a criterion of positive definiteness.- Matrix boundary value problems with eigenvalue dependent boundary conditions (The linear case).- Weyl-Titchmarsh functions of the canonical periodical system of differential equations.- On boundary values of functions regular in a disk.

Operator Theory and Boundary Eigenvalue Problems

I. Gohberg,H. Langer
Operator Theory and Boundary Eigenvalue Problems Book PDF

Author : I. Gohberg,H. Langer
Publisher : Birkhäuser
Page : 327 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034891066

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Operator Theory and Boundary Eigenvalue Problems by I. Gohberg,H. Langer Pdf

The Workshop on Operator Theory and Boundary Eigenvalue Problems was held at the Technical University, Vienna, Austria, July 27 to 30, 1993. It was the seventh workshop in the series of IWOTA (International Workshops on Operator Theory and Applications). The main topics at the workshop were interpolation problems and analytic matrix functions, operator theory in spaces with indefinite scalar products, boundary value problems for differential and functional-differential equations and systems theory and control. The workshop covered different aspects, starting with abstract operator theory up to contrete applications. The papers in these proceedings provide an accurate cross section of the lectures presented at the workshop. This book will be of interest to a wide group of pure and applied mathematicians.

Matrix and Operator Valued Functions

I. Gohberg,L.A. Sakhnovich
Matrix and Operator Valued Functions Book PDF

Author : I. Gohberg,L.A. Sakhnovich
Publisher : Birkhäuser
Page : 241 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885324

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Matrix and Operator Valued Functions by I. Gohberg,L.A. Sakhnovich Pdf

A collection of papers on different aspects of operator theory and complex analysis, covering the recent achievements of the Odessa-Kharkov school, where Potapov was very active. The book appeals to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.

New Aspects in Interpolation and Completion Theories

I. Gohberg
New Aspects in Interpolation and Completion Theories Book PDF

Author : I. Gohberg
Publisher : Birkhäuser
Page : 229 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034885621

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New Aspects in Interpolation and Completion Theories by I. Gohberg Pdf

This volume consists of eight papers containing recent advances in interpolation theory for matrix functions and completion theory for matrices and operators. In the first paper, D. Alpay and P. Loubaton, "The tangential trigonometric moment problem on an interval and related topics" a trigonometric moment problem on an interval for matrix valued functions is studied. The realization approach plays an important role in solving this problem. The second paper, M. Bakonyi, V.G. Kaftal, G. Weiss and H.J. Woerdeman, "Max imum entropy and joint norm bounds for operator extensions" is dedicated to a matrix completion problem. In it is considered the problem when only the lower triangular part of the operator entries of a matrix is identified. Completions which have simultaneously a small usual norm and a small Hilbert-Schmidt norm are considered. Bounds for these norms are obtained. The analysis of the maximum entropy extension plays a special role. The paper contains applications to nest algebras and integral operators. The third paper, J .A. Ball, I. Gohberg and M.A. Kaashoek, "Bitangential interpola tion for input-output operators of time varying systems: the discrete time case" contains solutions of time varying interpolation problems. The main attention is focused on the time varying analog of the Nevanlinna-Pick tangential problem in the case where the inter polation conditions appear from two sides. The state space theory of time varying systems play an important role.

Differentiable Operators and Nonlinear Equations

Victor Khatskevich,David Shoiykhet
Differentiable Operators and Nonlinear Equations Book PDF

Author : Victor Khatskevich,David Shoiykhet
Publisher : Birkhäuser
Page : 290 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885126

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Differentiable Operators and Nonlinear Equations by Victor Khatskevich,David Shoiykhet Pdf

The need to study holomorphic mappings in infinite dimensional spaces, in all likelihood, arose for the first time in connection with the development of nonlinear analysis. A systematic study of integral equations with an analytic nonlinear part was started at the end of the 19th and the beginning of the 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods, which subsequently have been refined and developed. Parallel with these achievements, the theory of functions of one or several complex variables was gradually enriched with more significant and subtle results. The present book is a first step towards establishing a bridge between nonlinear analysis, nonlinear operator equations and the theory of holomorphic mappings on Banach spaces. The work concludes with a brief exposition of the theory of spaces with indefinite metrics, and some relevant applications of the holomorphic mappings theory in this setting. In order to make this book accessible not only to specialists but also to students and engineers, the authors give a complete account of definitions and proofs, and also present relevant prerequisites from functional analysis and topology. Contents: Preliminaries • Differential calculus in normed spaces • Integration in normed spaces • Holomorphic (analytic) operators and vector-functions on complex Banach spaces • Linear operators • Nonlinear equations with differentiable operators • Nonlinear equations with holomorphic operators • Banach manifolds • Non-regular solutions of nonlinear equations • Operators on spaces with indefinite metric • References • List of Symbols • Subject Index.

Operator Extensions, Interpolation of Functions, and Related Topics

Aurelian Gheondea,Dan Timotin,Florian-Horia Vasilescu
Operator Extensions Interpolation of Functions and Related Topics Book PDF

Author : Aurelian Gheondea,Dan Timotin,Florian-Horia Vasilescu
Publisher : Unknown
Page : 212 pages
File Size : 40,7 Mb
Release : 1993
Category : Electronic books
ISBN : OCLC:1328580911

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Operator Extensions, Interpolation of Functions, and Related Topics by Aurelian Gheondea,Dan Timotin,Florian-Horia Vasilescu Pdf

Since 1976 the Institute of Mathematics of the Romanian Academy (formerly the Department of Mathematics of INCREST) and the Faculty of Mathematics (formerly the Faculty of Sciences) of the University ofTimi~oara have organized several Con ferences on Operator Theory. These Conferences were held yearly in Timi~oara (or in Timi~oara and Herculane) and beginning with 1985 they were held in Bucharest (1985,1986), in Timi~oara (1988) and in Predeal (1990). At the beginning, these Conferences answered the need of a part of the Romanian Mathematical Community ofexploring other forms of survival, after the dissolution of the Institute of Mathematics in 1975. Soon, these meetings evolved to International Conferences with a broad participation and where important results in Operator Theory and Operator Algebras and their interplay with Complex Function Theory, Differential Equations, Mathematical Physics, System Theory, etc. were presented. The 14th Conference on Operator Theory was held between June 1st and June 5th 1992, at the University ofTimi~oara. It was partially supported by the Institute of Mathematics of the Romanian Academy and by the Faculty of Mathematics of the University ofTimi~oara. Another important contribution towards covering the costs of this meeting came from The Soros Foundation for an Open Society. Without this generous help the organizing of this event would be impossible. Since 1980, the Proceedings of OT Conferences were published by Birkhauser Verlag in the series Operator Theory: Advances and Applications. The abstracts of the talks were collected in the Conference Report, published by the University of Timi~oara.

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

Daniel Alpay,Aad Dijksma,James Rovnyak,Hendrik de Snoo
Schur Functions Operator Colligations and Reproducing Kernel Pontryagin Spaces Book PDF

Author : Daniel Alpay,Aad Dijksma,James Rovnyak,Hendrik de Snoo
Publisher : Birkhäuser
Page : 244 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889087

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Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces by Daniel Alpay,Aad Dijksma,James Rovnyak,Hendrik de Snoo Pdf

Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.

Extensions of Positive Definite Functions

Palle Jorgensen,Steen Pedersen,Feng Tian
Extensions of Positive Definite Functions Book PDF

Author : Palle Jorgensen,Steen Pedersen,Feng Tian
Publisher : Springer
Page : 231 pages
File Size : 41,8 Mb
Release : 2016-07-08
Category : Mathematics
ISBN : 9783319397801

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Extensions of Positive Definite Functions by Palle Jorgensen,Steen Pedersen,Feng Tian Pdf

This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed group. It is therefore both an art and a science to produce solid conclusions from restricted or limited data. While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.

Classes of Linear Operators

Israel Gohberg,Seymour Goldberg,Marius A. Kaashoek
Classes of Linear Operators Book PDF

Author : Israel Gohberg,Seymour Goldberg,Marius A. Kaashoek
Publisher : Birkhäuser
Page : 563 pages
File Size : 55,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783034885584

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Classes of Linear Operators by Israel Gohberg,Seymour Goldberg,Marius A. Kaashoek Pdf

These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and unexpectedly. The result is a beautiful, unified and powerful theory. The classes we have chosen are representatives of the principal important classes of operators, and we believe that these illustrate the richness of operator theory, both in its theoretical developments and in its applicants. Because we wanted the books to be of reasonable size, we were selective in the classes we chose and restricted our attention to the main features of the corresponding theories. However, these theories have been updated and enhanced by new developments, many of which appear here for the first time in an operator-theory text. In the selection of the material the taste and interest of the authors played an important role.

Harmonic Analysis and Boundary Value Problems in the Complex Domain

Mkhitar M. Djrbashian
Harmonic Analysis and Boundary Value Problems in the Complex Domain Book PDF

Author : Mkhitar M. Djrbashian
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 45,5 Mb
Release : 1993
Category : Mathematics
ISBN : 376432855X

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Harmonic Analysis and Boundary Value Problems in the Complex Domain by Mkhitar M. Djrbashian Pdf

1 Preliminary results. Integral transforms in the complex domain.- 1.1 Introduction.- 1.2 Some identities.- 1.3 Integral representations and asymptotic formulas.- 1.4 Distribution of zeros.- 1.5 Identities between some Mellin transforms.- 1.6 Fourier type transforms with Mittag-Leffler kernels.- 1.7 Some consequences.- 1.8 Notes.- 2 Further results. Wiener-Paley type theorems.- 2.1 Introduction.- 2.2 Some simple generalizations of the first fundamental Wiener-Paley theorem.- 2.3 A general Wiener-Paley type theorem and some particular results.- 2.4 Two important cases of the general Wiener-Paley type theorem.- 2.5 Generalizations of the second fundamental Wiener-Paley theorem.- 2.6 Notes.- 3 Some estimates in Banach spaces of analytic functions.- 3.1 Introduction.- 3.2 Some estimates in Hardy classes over a half-plane.- 3.3 Some estimates in weighted Hardy classes over a half-plane.- 3.4 Some estimates in Banach spaces of entire functions of exponential type.- 3.5 Notes.- 4 Interpolation series expansions in spacesW1/2, ?p, ?of entire functions.- 4.1 Introduction.- 4.2 Lemmas on special Mittag-Leffler type functions.- 4.3 Two special interpolation series.- 4.4 Interpolation series expansions.- 4.5 Notes.- 5 Fourier type basic systems inL2(0, ?).- 5.1 Introduction.- 5.2 Biorthogonal systems of Mittag-Leffler type functions and their completeness inL2(0, ?).- 5.3 Fourier series type biorthogonal expansions inL2(0, ?).- 5.4 Notes.- 6 Interpolation series expansions in spacesWs+1/2, ?p, ?of entire functions.- 6.1 Introduction.- 6.2 The formulation of the main theorems.- 6.3 Auxiliary relations and lemmas.- 6.4 Further auxiliary results.- 6.5 Proofs of the main theorems.- 6.6 Notes.- 7 Basic Fourier type systems inL2spaces of odd-dimensional vector functions.- 7.1 Introduction.- 7.2 Some identities.- 7.3 Biorthogonal systems of odd-dimensional vector functions.- 7.4 Theorems on completeness and basis property.- 7.5 Notes.- 8 Interpolation series expansions in spacesWs, ?p, ?of entire functions.- 8.1 Introduction.- 8.2 The formulation of the main interpolation theorem.- 8.3 Auxiliary relations and lemmas.- 8.4 Further auxiliary results.- 8.5 The proof of the main interpolation theorem.- 8.6 Notes.- 9 Basic Fourier type systems inL2spaces of even-dimensional vector functions.- 9.1 Introduction.- 9.2 Some identities.- 9.3 The construction of biorthogonal systems of even-dimensional vector functions.- 9.4 Theorems on completeness and basis property.- 9.5 Notes.- 10 The simplest Cauchy type problems and the boundary value problems connected with them.- 10.1 Introduction.- 10.2 Riemann-Liouville fractional integrals and derivatives.- 10.3 A Cauchy type problem.- 10.4 The associated Cauchy type problem and the analog of Lagrange formula.- 10.5 Boundary value problems and eigenfunction expansions.- 10.6 Notes.- 11 Cauchy type problems and boundary value problems in the complex domain (the case of odd segments).- 11.1 Introduction.- 11.2 Preliminaries.- 11.3 Cauchy type problems and boundary value problems containing the operators $$ {\mathbb{L}_{s + 1/2}}$$ and $$ \mathbb{L}_{s + 1/2} *$$.- 11.4 Expansions inL2{?2s+1(?)} in terms of Riesz bases.- 11.5 Notes.- 12 Cauchy type problems and boundary value problems in the complex domain (the case of even segments).- 12.1 Introduction.- 12.2 Preliminaries.- 12.3 Cauchy type problems and boundary value problems containing the operators $${{\mathbb{L}}_{s}} $$ and $$ \mathbb{L}_{s} *$$.- 12.4 Expansions inL2{?2s(?)} in terms of Riesz bases.- 12.5

Contributions to Operator Theory and Its Applications

Takayuki Furuta,Israel Gohberg,Takahiko Nakazi
Contributions to Operator Theory and Its Applications Book PDF

Author : Takayuki Furuta,Israel Gohberg,Takahiko Nakazi
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 52,9 Mb
Release : 1993
Category : Mathematics
ISBN : 3764329289

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Contributions to Operator Theory and Its Applications by Takayuki Furuta,Israel Gohberg,Takahiko Nakazi Pdf

On Certain (Nearly) Convex Joint Numerical Ranges.- The Two-Sided Nevanlinna-Pick Problem in the Stieltjes Class.- State Space Formulas for Coprime Factorizations.- Generalization of Heinz-Kato Theorem via Furuta Inequality.- The Band Method for Bordered Algebras.- Lp-Distance Between Unitary Orbits in Type III? Factors.- Finite Dimensional Solution Sets of Extremal Problems in H1.- Factorization of Operators with Angularly Constrained Spectra.- On the Coefficients of Riemann Mappings on the Unit Disk into Itself.- Weak-Star Limits of Polynomials and their Derivatives.- Hausdorff Dimension of Some Fractals and Perron-Frobenius Theory.- Operators Which have Commutative Polar Decompositions.- Trace Formula for the Perturbation of Partial Differential Operator and Cyclic Cocycle on a Generalized Heisenberg Group.