Introduction To Hp Spaces
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| Author | : Paul Koosis |
| Publisher | : Cambridge University Press |
| Total Pages | : 316 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0521455219 |
The first edition of this well known book was noted for its clear and accessible exposition of the basic theory of Hardy spaces from the concrete point of view (in the unit circle and the half plane). The intention was to give the reader, assumed to know basic real and complex variable theory and a little functional analysis, a secure foothold in the basic theory, and to understand its applications in other areas. For this reason, emphasis is placed on methods and the ideas behind them rather than on the accumulation of as many results as possible. The second edition retains that intention, but the coverage has been extended. The author has included two appendices by V. P. Havin, on Peter Jones' interpolation formula, and Havin's own proof of the weak sequential completeness of L1/H1(0); in addition, numerous amendments, additions and corrections have been made throughout.
| Author | : Ruben A. Martinez-Avendano |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 230 |
| Release | : 2007-03-12 |
| Genre | : Mathematics |
| ISBN | : 0387485783 |
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
| Author | : Elias M. Stein |
| Publisher | : Princeton University Press |
| Total Pages | : 312 |
| Release | : 2016-06-02 |
| Genre | : Mathematics |
| ISBN | : 140088389X |
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
| Author | : Shanzhen Lu |
| Publisher | : World Scientific |
| Total Pages | : 226 |
| Release | : 1995-05-09 |
| Genre | : Mathematics |
| ISBN | : 9814500879 |
This book introduces the real variable theory of HP spaces briefly and concentrates on its applications to various aspects of analysis fields. It consists of four chapters. Chapter 1 introduces the basic theory of Fefferman-Stein on real HP spaces. Chapter 2 describes the atomic decomposition theory and the molecular decomposition theory of real HP spaces. In addition, the dual spaces of real HP spaces, the interpolation of operators in HP spaces, and the interpolation of HP spaces are also discussed in Chapter 2. The properties of several basic operators in HP spaces are discussed in Chapter 3 in detail. Among them, some basic results are contributed by Chinese mathematicians, such as the decomposition theory of weak HP spaces and its applications to the study on the sharpness of singular integrals, a new method to deal with the elliptic Riesz means in HP spaces, and the transference theorem of HP-multipliers etc. The last chapter is devoted to applications of real HP spaces to approximation theory.
| Author | : Jonathan R. Partington |
| Publisher | : Cambridge University Press |
| Total Pages | : 113 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : 0521366119 |
Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
| Author | : Emmanuel Fricain |
| Publisher | : Cambridge University Press |
| Total Pages | : 703 |
| Release | : 2016-05-26 |
| Genre | : Mathematics |
| ISBN | : 1316060918 |
An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.
| Author | : Yitzhak Katznelson |
| Publisher | : Cambridge University Press |
| Total Pages | : 342 |
| Release | : 2004-01-05 |
| Genre | : Mathematics |
| ISBN | : 9780521543590 |
| Author | : Emmanuel Fricain |
| Publisher | : Cambridge University Press |
| Total Pages | : 703 |
| Release | : 2016-05-26 |
| Genre | : Mathematics |
| ISBN | : 1107027772 |
This is volume 1 of a 2 volume set.
| Author | : Haim Brezis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 600 |
| Release | : 2010-11-02 |
| Genre | : Mathematics |
| ISBN | : 0387709142 |
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
| Author | : Stephan Ramon Garcia |
| Publisher | : Cambridge University Press |
| Total Pages | : 339 |
| Release | : 2016-05-17 |
| Genre | : Mathematics |
| ISBN | : 1316390438 |
The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.
