An Advanced Complex Analysis Problem Book

Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions

Author: Daniel Alpay

Publisher: Birkhäuser

ISBN: 3319160591

Category: Mathematics

Page: 521

View: 8375

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This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.
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A Complex Analysis Problem Book

Author: Daniel Alpay

Publisher: Birkhäuser

ISBN: 3319421816

Category: Mathematics

Page: 596

View: 950

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This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.
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Slice Hyperholomorphic Schur Analysis

Author: Daniel Alpay,Fabrizio Colombo,Irene Sabadini

Publisher: Birkhäuser

ISBN: 3319425145

Category: Mathematics

Page: 362

View: 4584

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This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research.
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Bounded Analytic Functions

Author: John Garnett

Publisher: Springer Science & Business Media

ISBN: 0387497633

Category: Mathematics

Page: 463

View: 4888

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This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. While paying proper attention to each of the three aspects, the author has underscored the effectiveness of the methods coming from real analysis, many of them developed as part of a program to extend the theory to Euclidean spaces, where the complex methods are not available.
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Advanced Real Analysis

Author: Anthony W. Knapp

Publisher: Springer Science & Business Media

ISBN: 9780817644420

Category: Mathematics

Page: 466

View: 7563

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* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
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Topological Vector Spaces, Distributions and Kernels

Author: Francois Treves

Publisher: Courier Corporation

ISBN: 0486453529

Category: Mathematics

Page: 565

View: 9915

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Extending beyond the boundaries of Hilbert and Banach space theory, this text focuses on key aspects of functional analysis, particularly in regard to solving partial differential equations. 1967 edition.
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American Book Publishing Record Cumulative, 1970-1974

Author: Bowker Editorial Staff

Publisher: N.A

ISBN: 9780835209113

Category:

Page: 6500

View: 8910

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Here's quick access to more than 490,000 titles published from 1970 to 1984 arranged in Dewey sequence with sections for Adult and Juvenile Fiction. Author and Title indexes are included, and a Subject Guide correlates primary subjects with Dewey and LC classification numbers. These cumulative records are available in three separate sets.
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Choice

A Classified Cumulation : Volumes 1-10, March 1964--February 1974

Author: Richard K. Gardner,Phyllis Grumm

Publisher: N.A

ISBN: N.A

Category: Best books

Page: N.A

View: 9748

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Composition Operators on Function Spaces

Author: R.K. Singh,J.S. Manhas

Publisher: Elsevier

ISBN: 9780080872902

Category: Mathematics

Page: 314

View: 602

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This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics. After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed. This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers.
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Applied Functional Analysis

Numerical Methods, Wavelet Methods, and Image Processing

Author: Abul Hasan Siddiqi

Publisher: CRC Press

ISBN: 0824756622

Category: Mathematics

Page: 660

View: 9997

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The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and numerical methods in infinite-dimensional spaces. This reference highlights critical studies in projection theorem, Riesz representation theorem, and properties of operators in Hilbert space and covers special classes of optimization problems. Supported by 2200 display equations, this guide incorporates hundreds of up-to-date citations.
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