Function Theory on Planar Domains
Function Theory on Planar Domains

Author: Stephen D. Fisher

Publisher: Courier Corporation

Published: 2007-02-27

Total Pages: 292

ISBN-13: 0486457680

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A high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.

Function Theory on Planar Domains
Function Theory on Planar Domains

Author: Stephen D. Fisher

Publisher: Courier Corporation

Published: 2014-06-10

Total Pages: 292

ISBN-13: 0486151107

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A high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.

Function-theoretic Operator Theory on Finitely Connected Planar Domains
Function-theoretic Operator Theory on Finitely Connected Planar Domains

Author: Vinh-Thy Minh Tran

Publisher:

Published: 1998

Total Pages:

ISBN-13:

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We generalize to finitely connected planar domains some classical results concerning composition operators and Toeplitz operators on the Hardy space and Bergman space of the unit disc. In particular, we study how operator-theoretic issues such as compactness and membership in Schattan classes are connected to function-theoretic issues such a value distribution, angular derivatives, and average growth near the boundary. In the process, we also obtain some boundary estimates involving the decay of the Green's function and the growth of certain reproducing kernels.

Hyponormal Quantization of Planar Domains
Hyponormal Quantization of Planar Domains

Author: Björn Gustafsson

Publisher: Springer

Published: 2017-09-29

Total Pages: 152

ISBN-13: 3319658107

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This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established. The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.

Geometric Function Theory
Geometric Function Theory

Author: Steven G. Krantz

Publisher: Springer Science & Business Media

Published: 2007-09-19

Total Pages: 311

ISBN-13: 0817644407

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* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations

Systems, Approximation, Singular Integral Operators, and Related Topics
Systems, Approximation, Singular Integral Operators, and Related Topics

Author: Alexander A. Borichev

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 536

ISBN-13: 3034883625

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This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.

Functions of One Complex Variable II
Functions of One Complex Variable II

Author: John B. Conway

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 404

ISBN-13: 1461208173

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This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric function theory as well as potential theory in the plane, covering in particular: conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions, analytic covering maps, de Branges' proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, potential theory in the plane. A knowledge of integration theory and functional analysis is assumed.

Function Spaces
Function Spaces

Author: Krzysztof Jarosz

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 330

ISBN-13: 0821832697

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This volume presents papers from the Fourth Conference on Function Spaces. The conference brought together mathematicians interested in various problems within the general area of function spaces, allowing for discussion and exchange of ideas on those problems and related questions. The lectures covered a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $Lp$-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and related subjects. Included are 26 articles written by leading experts. Known results, open problems, and new discoveries are featured. Most papers are written for nonexperts, so the book can serve as a good introduction to the material presented.

Subnormal Operators and Representations of Algebras of Bounded Analytic Functions and Other Uniform Algebras
Subnormal Operators and Representations of Algebras of Bounded Analytic Functions and Other Uniform Algebras

Author: Thomas L. Miller

Publisher: American Mathematical Soc.

Published: 1986

Total Pages: 137

ISBN-13: 0821824155

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The present memoir lies between operator theory and function theory of one complex variable. Motivated by refinements of the analytic functional calculus of a subnormal operator, the authors are rapidly directed towards difficult problems of hard analysis. Quite specifically, the basic objects to be investigated in this paper are the unital (continuous) algebra homomorphisms [lowercase Greek]Pi : [italic]H[exponent infinity symbol]([italic]G) [rightwards arrow] [italic]L([italic]H), with the additional property that [lowercase Greek]Pi([italic]z) is a subnormal operator.