Interpolation Of Operators

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Interpolation of Operators

Colin Bennett,Robert C. Sharpley
Interpolation of Operators Book PDF

Author : Colin Bennett,Robert C. Sharpley
Publisher : Academic Press
Page : 469 pages
File Size : 54,7 Mb
Release : 1988-04-01
Category : Mathematics
ISBN : 0080874487

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Interpolation of Operators by Colin Bennett,Robert C. Sharpley Pdf

This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis. The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.

Interpolation of Linear Operators

S. G. Krein,E. M. Semenov
Interpolation of Linear Operators Book PDF

Author : S. G. Krein,E. M. Semenov
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 49,6 Mb
Release : 2002-10-21
Category : Mathematics
ISBN : 9780821831762

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Interpolation of Linear Operators by S. G. Krein,E. M. Semenov Pdf

Operator Theory and Interpolation

Hari Bercovic,Ciprian I. Foias
Operator Theory and Interpolation Book PDF

Author : Hari Bercovic,Ciprian I. Foias
Publisher : Birkhäuser
Page : 311 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884228

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Operator Theory and Interpolation by Hari Bercovic,Ciprian I. Foias Pdf

A collection of articles emphasizing modern interpolation theory, a topic which has seen much progress in recent years. These ideas and problems in operator theory, often arising from systems and control theories, bring the reader to the forefront of current research in this area.

Topics in Operator Theory and Interpolation

I. Gohberg
Topics in Operator Theory and Interpolation Book PDF

Author : I. Gohberg
Publisher : Birkhäuser
Page : 240 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034891622

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Topics in Operator Theory and Interpolation by I. Gohberg Pdf

Global Smoothness and Shape Preserving Interpolation by Classical Operators

Sorin Gal
Global Smoothness and Shape Preserving Interpolation by Classical Operators Book PDF

Author : Sorin Gal
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 42,6 Mb
Release : 2005-07-27
Category : Mathematics
ISBN : 0817643877

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Global Smoothness and Shape Preserving Interpolation by Classical Operators by Sorin Gal Pdf

This monograph examines in detail two aspects in the field of interpolation of functions -the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP). By considering well-known classical interpolation operators such as Lagrange, Grünwald, Hermite-Fejér and Shepard type, the study is mainly developed for the univariate and bivariate cases. One of the first books on the subject, it presents to the reader, recent work featuring many new interesting results in this field, including an excellent survey of past research. Accompanied by numerous open problems, an updated set of references, and an appendix featuring illustrations of nine types of Shepard surfaces, this unique text is best suited to graduate students and researchers in mathematical analysis, interpolation of functions, pure and applied mathematicians in numerical analysis, approximation theory, data fitting, computer aided geometric design, fluid mechanics, and engineering researchers.

Interpolation Spaces

J. Bergh,J. Löfström
Interpolation Spaces Book PDF

Author : J. Bergh,J. Löfström
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642664519

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Interpolation Spaces by J. Bergh,J. Löfström Pdf

The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boe1 Engebrand, Lena Mattsson and Birgit Hoglund for their expert typing of our manuscript.

Interpolation Theory and Applications

Michael Cwikel,Laura De Carli,Mario Milman
Interpolation Theory and Applications Book PDF

Author : Michael Cwikel,Laura De Carli,Mario Milman
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 47,7 Mb
Release : 2007
Category : Interpolation
ISBN : 9780821842072

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Interpolation Theory and Applications by Michael Cwikel,Laura De Carli,Mario Milman Pdf

This volume contains the Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). The central topic of this book is interpolation theory in its broadest sense, with special attention to its applications to analysis. The articles include applications to classical analysis, harmonic analysis, partial differential equations, function spaces, image processing, geometry of Banach spaces, and more. This volume emphasizes remarkable connections between several branches of pure and applied analysis. Graduate students and researchers in analysis will find it very useful.

Metric Constrained Interpolation, Commutant Lifting and Systems

C. Foias,A.E. Frezho,I. Gohberg,M.A. Kaashoek
Metric Constrained Interpolation Commutant Lifting and Systems Book PDF

Author : C. Foias,A.E. Frezho,I. Gohberg,M.A. Kaashoek
Publisher : Birkhäuser
Page : 587 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887915

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Metric Constrained Interpolation, Commutant Lifting and Systems by C. Foias,A.E. Frezho,I. Gohberg,M.A. Kaashoek Pdf

This book presents a unified approach for solving both stationary and nonstationary interpolation problems, in finite or infinite dimensions, based on the commutant lifting theorem from operator theory and the state space method from mathematical system theory. Initially the authors planned a number of papers treating nonstationary interpolation problems of Nevanlinna-Pick and Nehari type by reducing these nonstationary problems to stationary ones for operator-valued functions with operator arguments and using classical commutant lifting techniques. This reduction method required us to review and further develop the classical results for the stationary problems in this more general framework. Here the system theory turned out to be very useful for setting up the problems and for providing natural state space formulas for describing the solutions. In this way our work involved us in a much wider program than original planned. The final results of our efforts are presented here. The financial support in 1994 from the "NWO-stimulansprogramma" for the Thomas Stieltjes Institute for Mathematics in the Netherlands enabled us to start the research which lead to the present book. We also gratefully acknowledge the support from our home institutions: Indiana University at Bloomington, Purdue University at West Lafayette, Tel-Aviv University, and the Vrije Universiteit at Amsterdam. We warmly thank Dr. A.L. Sakhnovich for his carefully reading of a large part of the manuscript. Finally, Sharon Wise prepared very efficiently and with great care the troff file of this manuscript; we are grateful for her excellent typing.

Complex Interpolation between Hilbert, Banach and Operator Spaces

Gilles Pisier
Complex Interpolation between Hilbert Banach and Operator Spaces Book PDF

Author : Gilles Pisier
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 50,7 Mb
Release : 2010-10-07
Category : Mathematics
ISBN : 9780821848425

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Complex Interpolation between Hilbert, Banach and Operator Spaces by Gilles Pisier Pdf

Motivated by a question of Vincent Lafforgue, the author studies the Banach spaces $X$ satisfying the following property: there is a function $\varepsilon\to \Delta_X(\varepsilon)$ tending to zero with $\varepsilon>0$ such that every operator $T\colon \ L_2\to L_2$ with $\T\\le \varepsilon$ that is simultaneously contractive (i.e., of norm $\le 1$) on $L_1$ and on $L_\infty$ must be of norm $\le \Delta_X(\varepsilon)$ on $L_2(X)$. The author shows that $\Delta_X(\varepsilon) \in O(\varepsilon^\alpha)$ for some $\alpha>0$ iff $X$ is isomorphic to a quotient of a subspace of an ultraproduct of $\theta$-Hilbertian spaces for some $\theta>0$ (see Corollary 6.7), where $\theta$-Hilbertian is meant in a slightly more general sense than in the author's earlier paper (1979).

Global Smoothness and Shape Preserving Interpolation by Classical Operators

Sorin G. Gal
Global Smoothness and Shape Preserving Interpolation by Classical Operators Book PDF

Author : Sorin G. Gal
Publisher : Springer Science & Business Media
Page : 155 pages
File Size : 40,9 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9780817644017

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Global Smoothness and Shape Preserving Interpolation by Classical Operators by Sorin G. Gal Pdf

This monograph examines in detail two aspects in the field of interpolation of functions -the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP). By considering well-known classical interpolation operators such as Lagrange, Grünwald, Hermite-Fejér and Shepard type, the study is mainly developed for the univariate and bivariate cases. One of the first books on the subject, it presents to the reader, recent work featuring many new interesting results in this field, including an excellent survey of past research. Accompanied by numerous open problems, an updated set of references, and an appendix featuring illustrations of nine types of Shepard surfaces, this unique text is best suited to graduate students and researchers in mathematical analysis, interpolation of functions, pure and applied mathematicians in numerical analysis, approximation theory, data fitting, computer aided geometric design, fluid mechanics, and engineering researchers.