On Interpolation Of Operators
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Author | : Colin Bennett |
Publisher | : Academic Press |
Total Pages | : 489 |
Release | : 1988-04-01 |
Genre | : Mathematics |
ISBN | : 0080874487 |
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 | : S. G. Krein |
Publisher | : American Mathematical Soc. |
Total Pages | : 390 |
Release | : 2002-10-21 |
Genre | : Mathematics |
ISBN | : 0821831763 |
Author | : Hans Triebel |
Publisher | : |
Total Pages | : 540 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : |
Author | : J. Bergh |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642664512 |
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 | : Joongwhee Kim |
Publisher | : |
Total Pages | : 134 |
Release | : 1999 |
Genre | : Operator theory |
ISBN | : |
Author | : Barbara Gail Frazier |
Publisher | : |
Total Pages | : 36 |
Release | : 1987 |
Genre | : Operator equations |
ISBN | : |
Author | : Kristian Seip |
Publisher | : American Mathematical Soc. |
Total Pages | : 153 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821835548 |
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 | : Jim Agler |
Publisher | : American Mathematical Society |
Total Pages | : 330 |
Release | : 2023-02-22 |
Genre | : Mathematics |
ISBN | : 1470468557 |
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 | : Alessandra Lunardi |
Publisher | : Springer |
Total Pages | : 208 |
Release | : 2018-05-05 |
Genre | : Mathematics |
ISBN | : 8876426388 |
This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.
Author | : I. Gohberg |
Publisher | : Birkhäuser |
Total Pages | : 311 |
Release | : 2013-11-11 |
Genre | : Science |
ISBN | : 3034877013 |