Interpolation Spaces

Author : Anonim
Publisher : Elsevier
Page : 717 pages
File Size : 51,6 Mb
Release : 1991-03-18
Category : Mathematics
ISBN : 0080887104

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Interpolation Functors and Interpolation Spaces by Anonim Pdf

The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the results of that solution, as well as drawing heavily on a classic paper by Aronszajn and Gagliardo, which appeared in 1965 but whose real importance was not realized until a decade later. This includes a systematic use of the language, if not the theory, of categories. In this way the book also opens up many new vistas which still have to be explored. This volume is the first of three planned books. Volume II will deal with the complex method, while Volume III will deal with applications.

Author : Luc Tartar
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 54,7 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9783540714835

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An Introduction to Sobolev Spaces and Interpolation Spaces by Luc Tartar Pdf

After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.

Author : J. Bergh,J. Löfström
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 43,9 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.

Author : M. Cwikel,J. Peetre
Publisher : Springer
Page : 245 pages
File Size : 51,8 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540389132

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Interpolation Spaces and Allied Topics in Analysis by M. Cwikel,J. Peetre Pdf

Author : Jim Agler,John E. McCarthy
Publisher : American Mathematical Society
Page : 330 pages
File Size : 44,8 Mb
Release : 2023-02-22
Category : Mathematics
ISBN : 9781470468552

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Pick Interpolation and Hilbert Function Spaces by Jim Agler,John E. McCarthy Pdf

The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.

Author : Michael Cwikel,Miroslav Englis,Alois Kufner,Lars-Erik Persson,Gunnar Sparr
Publisher : Walter de Gruyter
Page : 473 pages
File Size : 52,6 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110198058

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Function Spaces, Interpolation Theory and Related Topics by Michael Cwikel,Miroslav Englis,Alois Kufner,Lars-Erik Persson,Gunnar Sparr Pdf

This volume contains 16 refereed research articles on function spaces, interpolation theory and related fields. Topics covered: theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, special functions, homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets. The book will be of interest to both researchers and graduate students working in interpolation theory, function spaces and operators, partial differential equations and analysis on bounded symmetric domains.

Author : Michael Cwikel,Per G. Nilsson,Gideon Schechtman
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 48,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821833827

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Interpolation of Weighted Banach Lattices/A Characterization of Relatively Decomposable Banach Lattices by Michael Cwikel,Per G. Nilsson,Gideon Schechtman Pdf

Interpolation of Weighted Banach Lattices It is known that for many, but not all, compatible couples of Banach spaces $(A_{0},A_{1})$ it is possible to characterize all interpolation spaces with respect to the couple via a simple monotonicity condition in terms of the Peetre $K$-functional. Such couples may be termed Calderon-Mityagin couples. The main results of the present paper provide necessary and sufficient conditions on a couple of Banach lattices of measurable functions $(X_{0},X_{1})$ which ensure that, for all weight functions $w_{0}$ and $w_{1}$, the couple of weighted lattices $(X_{0,w_{0}},X_{1,w_{1}})$ is a Calderon-Mityagin couple. Similarly, necessary and sufficient conditions are given for two couples of Banach lattices $(X_{0},X_{1})$ and $(Y_{0},Y_{1})$ to have the property that, for all choices of weight functions $w_{0}, w_{1}, v_{0}$ and $v_{1}$, all relative interpolation spaces with respect to the weighted couples $(X_{0,w_{0}},X_{1,w_{1}})$ and $(Y_{0,v_{0}},Y_{1,v_{1}})$ may be described via an obvious analogue of the above-mentioned $K$-functional monotonicity condition. A number of auxiliary results developed in the course of this work can also be expected to be useful in other contexts. These include a formula for the $K$-functional for an arbitrary couple of lattices which offers some of the features of Holmstedt's formula for $K(t,f;L^{p},L^{q})$, and also the following uniqueness theorem for Calderon's spaces $X^{1-\theta }_{0}X^{\theta }_{1}$: Suppose that the lattices $X_0$, $X_1$, $Y_0$ and $Y_1$ are all saturated and have the Fatou property. If $X^{1-\theta }_{0}X^{\theta }_{1} = Y^{1-\theta }_{0}Y^{\theta }_{1}$ for two distinct values of $\theta $ in $(0,1)$, then $X_{0} = Y_{0}$ and $X_{1} = Y_{1}$. Yet another such auxiliary result is a generalized version of Lozanovskii's formula $\left( X_{0}^{1-\theta }X_{1}^{\theta }\right) ^{\prime }=\left (X_{0}^{\prime }\right) ^{1-\theta }\left( X_{1}^{\prime }\right) ^{\theta }$ for the associate space of $X^{1-\theta }_{0}X^{\theta }_{1}$. A Characterization of Relatively Decomposable Banach Lattices Two Banach lattices of measurable functions $X$ and $Y$ are said to be relatively decomposable if there exists a constant $D$ such that whenever two functions $f$ and $g$ can be expressed as sums of sequences of disjointly supported elements of $X$ and $Y$ respectively, $f = \sum^{\infty }_{n=1} f_{n}$ and $g = \sum^{\infty }_{n=1} g_{n}$, such that $\ g_{n}\ _{Y} \le \ f_{n}\ _{X}$ for all $n = 1, 2, \ldots $, and it is given that $f \in X$, then it follows that $g \in Y$ and $\ g\ _{Y} \le D\ f\ _{X}$. Relatively decomposable lattices appear naturally in the theory of interpolation of weighted Banach lattices. It is shown that $X$ and $Y$ are relatively decomposable if and only if, for some $r \in [1,\infty ]$, $X$ satisfies a lower $r$-estimate and $Y$ satisfies an upper $r$-estimate. This is also equivalent to the condition that $X$ and $\ell ^{r}$ are relatively decomposable and also $\ell ^{r}$ and $Y$ are relatively decomposable.

Author : Kristian Seip
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 55,7 Mb
Release : 2004
Category : Analytic functions
ISBN : 9780821835548

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Interpolation and Sampling in Spaces of Analytic Functions by Kristian Seip Pdf

Based on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's interpolation theorem, an

Author : Gilles Pisier
Publisher : American Mathematical Soc.
Page : 103 pages
File Size : 52,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804742

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The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms by Gilles Pisier Pdf

In the recently developed duality theory of operator spaces (as developed by Effros-Ruan and Blecher-Paulsen) bounded operators are replaced by completely bounded ones, isomorphisms by complete isomorphisms, and Banach spaces by operator spaces. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into $B(H)$ (with $H$ being Hilbert). In this new category, several operator spaces which are isomorphic (as Banach spaces) to a Hilbert space play an important role. For instance the row and column Hilbert spaces and several other examples appearing naturally in the construction of the Boson or Fermion Fock spaces have been studied extensively. One of the main results of this memoir is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (denoted by $OH$ ) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces. This new concept, called ``the operator Hilbert space'' and denoted by $OH$, is introduced and thoroughly studied in this volume.

Author : Michael Cwikel,Mario Milman,Richard Rochberg
Publisher : Unknown
Page : 316 pages
File Size : 55,8 Mb
Release : 1992
Category : Interpolation
ISBN : STANFORD:36105008528569

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Interpolation Spaces and Related Topics by Michael Cwikel,Mario Milman,Richard Rochberg Pdf

Author : Michael Cwikel,Yoram Sagher
Publisher : Unknown
Page : 244 pages
File Size : 50,7 Mb
Release : 1999
Category : Function spaces
ISBN : STANFORD:36105110506099

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Function Spaces, Interpolation Spaces, and Related Topics by Michael Cwikel,Yoram Sagher Pdf

This volume presents the proceedings of the international workshop held at the Technion-Israel Institute of Technology. Included are research and survey articles on interpolation theory and function spaces.

Author : Alexandru Aleman,Haakan Hedenmalm,Dmitry Khavinson,Mihai Putinar
Publisher : Springer
Page : 281 pages
File Size : 50,7 Mb
Release : 2019-05-30
Category : Mathematics
ISBN : 9783030146405

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Analysis of Operators on Function Spaces by Alexandru Aleman,Haakan Hedenmalm,Dmitry Khavinson,Mihai Putinar Pdf

This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.

Author : Colin Bennett,Robert C. Sharpley
Publisher : Academic Press
Page : 469 pages
File Size : 43,7 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.

Author : Michael Cwikel,Laura De Carli,Mario Milman
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 42,7 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.

Author : J. Bergh,Jorgen Lofstrom
Publisher : Springer
Page : 207 pages
File Size : 47,6 Mb
Release : 1976-11-20
Category : Mathematics
ISBN : 3540078754

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Interpolation Spaces by J. Bergh,Jorgen Lofstrom 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.