Theory Of Commuting Nonselfadjoint Operators

Author : Moshe S. Livšic
Publisher : Unknown
Page : 318 pages
File Size : 52,7 Mb
Release : 1995
Category : Nonselfadjoint operators
ISBN : OCLC:1328256439

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Theory of Commuting Nonselfadjoint Operators by Moshe S. Livšic Pdf

Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no ticed in 1952 that [49]: "The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra." Subsequently, spectral analysis has been developed for different classes of non selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve.

Author : M.S. Livsic,N. Kravitsky,A.S. Markus,V. Vinnikov
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 44,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401585613

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Theory of Commuting Nonselfadjoint Operators by M.S. Livsic,N. Kravitsky,A.S. Markus,V. Vinnikov Pdf

Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no ticed in 1952 that [49]: "The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra." Subsequently, spectral analysis has been developed for different classes of non selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve.

Author : M.S. Livsic,N. Kravitsky,A.S. Markus,V. Vinnikov
Publisher : Springer
Page : 318 pages
File Size : 40,7 Mb
Release : 2014-03-14
Category : Mathematics
ISBN : 9401585628

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Theory of Commuting Nonselfadjoint Operators by M.S. Livsic,N. Kravitsky,A.S. Markus,V. Vinnikov Pdf

Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no ticed in 1952 that [49]: "The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra." Subsequently, spectral analysis has been developed for different classes of non selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve.

Author : Moshe S. Livsic,Leonid L. Waksman
Publisher : Springer
Page : 116 pages
File Size : 49,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540478775

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Commuting Nonselfadjoint Operators in Hilbert Space by Moshe S. Livsic,Leonid L. Waksman Pdf

Classification of commuting non-selfadjoint operators is one of the most challenging problems in operator theory even in the finite-dimensional case. The spectral analysis of dissipative operators has led to a series of deep results in the framework of unitary dilations and characteristic operator functions. It has turned out that the theory has to be based on analytic functions on algebraic manifolds and not on functions of several independent variables as was previously believed. This follows from the generalized Cayley-Hamilton Theorem, due to M.S.Livsic: "Two commuting operators with finite dimensional imaginary parts are connected in the generic case, by a certain algebraic equation whose degree does not exceed the dimension of the sum of the ranges of imaginary parts." Such investigations have been carried out in two directions. One of them, presented by L.L.Waksman, is related to semigroups of projections of multiplication operators on Riemann surfaces. Another direction, which is presented here by M.S.Livsic is based on operator colligations and collective motions of systems. Every given wave equation can be obtained as an external manifestation of collective motions. The algebraic equation mentioned above is the corresponding dispersion law of the input-output waves.

Author : Daniel Alpay,Victor Vinnikov
Publisher : Birkhäuser
Page : 568 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882477

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Operator Theory, System Theory and Related Topics by Daniel Alpay,Victor Vinnikov Pdf

This volume presents the refereed proceedings of the Conference in Operator The ory in Honour of Moshe Livsic 80th Birthday, held June 29 to July 4, 1997, at the Ben-Gurion University of the Negev (Beer-Sheva, Israel) and at the Weizmann In stitute of Science (Rehovot, Israel). The volume contains papers in operator theory and its applications (understood in a very wide sense), many of them reflecting, 1 directly or indirectly, a profound impact of the work of Moshe Livsic. Moshe (Mikhail Samuilovich) Livsic was born on July 4, 1917, in the small town of Pokotilova near Uman, in the province of Kiev in the Ukraine; his family moved to Odessa when he was four years old. In 1933 he enrolled in the Department of Physics and Mathematics at the Odessa State University, where he became a student of M. G. Krein and an active participant in Krein's seminar - one of the centres where the ideas and methods of functional analysis and operator theory were being developed. Besides M. G. Krein, M. S. Livsic was strongly influenced B. Va. Levin, an outstanding specialist in the theory of analytic functions. A by deep understanding of operator theory as well as function theory and a penetrating search of connections between the two, were to become one of the landmarks of M. S. Livsic's work. M. S. Livsic defended his Ph. D.

Author : J. K. Aggarwal
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 50,7 Mb
Release : 1993-01-22
Category : Computers
ISBN : 376432824X

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Operator Theory and Complex Analysis by J. K. Aggarwal Pdf

This volume presents a set of papers based on the proceedings of the NATO Advanced Research Workshop on Multisensor Fusion for Computer Vision, held in Grenoble, France, in June 1989. The workshop focused on the fusion or integration of sensor information to achieve the optimum interpretation of a scene. The papers cover a broad range of topics, including principles and issues in multisensor fusion, information fusion for navigation, multisensor fusion for object recognition, network approaches to multisensor fusion, computer architectures for multisensor fusion, and applications of multisensor fusion. The authors have documented their own research and, in so doing,have presented the state of the art in the field. Each author is a recognized leader in his or her area in the academic, governmental, or industrial research community. Several contributors present novel points of view on the integration of information. The book gives a representative picture of current progress in multisensor fusion for computer vision among the leading research groups in Europe and North America.

Author : T. Ando,I. Gohberg
Publisher : Birkhäuser
Page : 417 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034886062

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Operator Theory and Complex Analysis by T. Ando,I. Gohberg Pdf

Author : Moshe S. Livsic,Leonid L. Waksman
Publisher : Unknown
Page : 124 pages
File Size : 43,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662163136

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Commuting Nonselfadjoint Operators in Hilbert Space by Moshe S. Livsic,Leonid L. Waksman Pdf

Author : A. Feintuch,I. Gohberg
Publisher : Birkhäuser
Page : 433 pages
File Size : 52,9 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.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 50,5 Mb
Release : 2007-11-23
Category : Mathematics
ISBN : 9780306483738

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Encyclopaedia of Mathematics, Supplement III by Michiel Hazewinkel Pdf

This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Author : Sheldon Jay Axler,John E. McCarthy,Donald Sarason
Publisher : Cambridge University Press
Page : 490 pages
File Size : 46,7 Mb
Release : 1998-05-28
Category : Mathematics
ISBN : 0521631939

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Holomorphic Spaces by Sheldon Jay Axler,John E. McCarthy,Donald Sarason Pdf

Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.

Author : Israel Gohberg,Yuri I. Lyubich
Publisher : Birkhäuser
Page : 269 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889100

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New Results in Operator Theory and Its Applications by Israel Gohberg,Yuri I. Lyubich Pdf

This volume is dedicated to the memory of Israel Glazman, an outstanding personality and distinguished mathematician, the author of many remarkable papers and books in operator theory and its applications. The present book opens with an essay devoted to Glazman's life and scientific achievements. It focusses on the areas of his unusually wide interests and consists of 18 mathematical papers in spectral theory of differential operators and linear operators in Hilbert and Banach spaces, analytic operator functions, ordinary and partial differential equations, functional equations, mathematical physics, nonlinear functional analysis, approximation theory and optimization, and mathematical statistics. The book gives a picture of the current state of some important problems in areas of operator theory and its applications and will be of interest to a wide group of researchers working in pure and applied mathematics.

Author : Daniel Alpay,Victor Vinnikov
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 50,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373030

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Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations by Daniel Alpay,Victor Vinnikov Pdf

This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Author : Joachim Rosenthal,David S. Gilliam
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9780387216966

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Mathematical Systems Theory in Biology, Communications, Computation and Finance by Joachim Rosenthal,David S. Gilliam Pdf

This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.

Author : Israel Gohberg,Mark Grigorʹevich Kreĭn
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 47,5 Mb
Release : 1978
Category : Mathematics
ISBN : 0821886509

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Introduction to the Theory of Linear Nonselfadjoint Operators by Israel Gohberg,Mark Grigorʹevich Kreĭn Pdf