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Author: Alexandru Aleman
Publisher: Springer Science & Business Media
ISBN: 3034600984
Category : Mathematics
Languages : en
Pages : 135
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Book Description
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 .
Author: Alexandru Aleman
Publisher: Springer Science & Business Media
ISBN: 3034600984
Category : Mathematics
Languages : en
Pages : 135
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Book Description
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 .
Author: Stephan Ramon Garcia
Publisher: Oxford University Press
ISBN: 019267885X
Category : Science
Languages : en
Pages : 529
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Book Description
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.
Author: Stephan Ramon Garcia
Publisher: Cambridge University Press
ISBN: 1316390438
Category : Mathematics
Languages : en
Pages : 339
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Book Description
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.
Author: American Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1170
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Book Description
Author: John B. Garnett
Publisher: Cambridge University Press
ISBN: 1139443097
Category : Mathematics
Languages : en
Pages : 4
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Book Description
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.
Author: Eric Grinberg
Publisher: American Mathematical Soc.
ISBN: 0821811487
Category : Mathematics
Languages : en
Pages : 524
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Book Description
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.
Author: Arthur James Wells
Publisher:
ISBN:
Category : Bibliography, National
Languages : en
Pages : 1922
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Book Description
Author: Klaus Gürlebeck
Publisher: Springer
ISBN: 3034809646
Category : Mathematics
Languages : en
Pages : 402
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Book Description
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.
Author: Juha Kinnunen
Publisher: American Mathematical Soc.
ISBN: 1470465752
Category : Education
Languages : en
Pages : 354
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Book Description
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.
Author: O. A. Ladyzhenskaya Anatoli_ Moiseevich Vershik
Publisher: American Mathematical Soc.
ISBN: 9780821895900
Category : Mathematics
Languages : en
Pages : 244
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Book Description
This is the inaugural volume of a new book series published under the auspices of the St. Petersburg Mathematical Society. The book contains contributions by some of the leading mathematicians in St. Petersburg. Ranging over a wide array of topics, these papers testify to the diverse interests and productive mathematical life of the St. Petersburg Mathematical Society.
