The Hardy Space Of A Slit Domain
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The Hardy Space Of A Slit Domain
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Author : Alexandru Aleman
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-08
The Hardy Space Of A Slit Domain written by Alexandru Aleman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-08 with Mathematics categories.
If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails both the properties z of the functions inside the domain G, their zero sets for example, as well as the behavior of the functions near the boundary of G. The operator M is not only interesting in its z own right but often serves as a model operator for certain classes of linear operators. By this we mean that given an operator T on H with certain properties (certain subnormal operators or two-isometric operators with the right spectral properties, etc. ), there is a Hilbert space of analytic functions on a domain G for which T is unitarity equivalent to M .
Analysis Geometry Number Theory The Mathematics Of Leon Ehrenpreis
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Author : Eric Grinberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Analysis Geometry Number Theory The Mathematics Of Leon Ehrenpreis written by Eric Grinberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book presents the proceedings from the conference honoring the work of Leon Ehrenpreis. Professor Ehrenpreis worked in many different areas of mathematics and found connections among all of them. For example, one can find his analytic ideas in the context of number theory, geometric thinking within analysis, transcendental number theory applied to partial differential equations, and more. The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work. The collection of articles here presents current research on PDEs, several complex variables, analytic number theory, integral geometry, and tomography. The work of Professor Ehrenpreis has contributed to basic definitions in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.
Harmonic Measure
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Author : John B. Garnett
language : en
Publisher: Cambridge University Press
Release Date : 2005-04-04
Harmonic Measure written by John B. Garnett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-04 with Mathematics categories.
During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback for the first time. The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and extremal length, and each chapter has many exercises to further inform and teach the readers.
Operator Theory By Example
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Author : Stephan Ramon Garcia
language : en
Publisher: Oxford University Press
Release Date : 2023-02-09
Operator Theory By Example written by Stephan Ramon Garcia and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Science categories.
Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator. The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.
Introduction To Model Spaces And Their Operators
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Author : Stephan Ramon Garcia
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-17
Introduction To Model Spaces And Their Operators written by Stephan Ramon Garcia and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-17 with Mathematics categories.
A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.
Maximal Function Methods For Sobolev Spaces
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Author : Juha Kinnunen
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-08-02
Maximal Function Methods For Sobolev Spaces written by Juha Kinnunen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Education categories.
This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
Application Of Holomorphic Functions In Two And Higher Dimensions
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Author : Klaus Gürlebeck
language : en
Publisher: Springer
Release Date : 2016-06-20
Application Of Holomorphic Functions In Two And Higher Dimensions written by Klaus Gürlebeck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.
This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.
Riemann Hilbert Problems Their Numerical Solution And The Computation Of Nonlinear Special Functions
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Author : Thomas Trogdon
language : en
Publisher: SIAM
Release Date : 2015-12-22
Riemann Hilbert Problems Their Numerical Solution And The Computation Of Nonlinear Special Functions written by Thomas Trogdon and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-22 with Mathematics categories.
Riemann?Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann?Hilbert problem.This book, the most comprehensive one to date on the applied and computational theory of Riemann?Hilbert problems, includes an introduction to computational complex analysis, an introduction to the applied theory of Riemann?Hilbert problems from an analytical and numerical perspective, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.?
The British National Bibliography
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Author : Arthur James Wells
language : en
Publisher:
Release Date : 2009
The British National Bibliography written by Arthur James Wells and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Bibliography, National categories.
Transactions Of The American Mathematical Society
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1994
Transactions Of The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.