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Author : Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher : American Mathematical Soc.
Page : 460 pages
File Size : 52,9 Mb
Release : 2002
Category : Control theory
ISBN : 0821828762
Author : Nikolai Kapitonovich Nikolskii
Publisher : Unknown
Page : 0 pages
File Size : 44,8 Mb
Release : 2002
Category : Electronic
ISBN : OCLC:860610855
Author : Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher : Unknown
Page : 439 pages
File Size : 42,5 Mb
Release : 2002
Category : Control theory
ISBN : LCCN:2001053556
Author : Nikolai K. Nikolski
Publisher : American Mathematical Soc.
Page : 458 pages
File Size : 48,7 Mb
Release : 2010-10-06
Category : Mathematics
ISBN : 9780821852651
Together with the companion volume by the same author, Operators, Functions, and Systems: An Easy Reading. Volume 1: Hardy, Hankel, and Toeplitz, Mathematical Surveys and Monographs, Vol. 92, AMS, 2002, this unique work combines four major topics of modern analysis and its applications: A. Hardy classes of holomorphic functions, B. Spectral theory of Hankel and Toeplitz operators, C. Function models for linear operators and free interpolations, and D. Infinite-dimensional system theory and signal processing. This volume contains Parts C and D. Function models for linear operators and free interpolations: This is a universal topic and, indeed, is the most influential operator theory technique in the post-spectral-theorem era. In this book, its capacity is tested by solving generalized Carleson-type interpolation problems. Infinite-dimensional system theory and signal processing: This topic is the touchstone of the three previously developed techniques. The presence of this applied topic in a pure mathematics environment reflects important changes in the mathematical landscape of the last 20 years, in that the role of the main consumer and customer of harmonic, complex, and operator analysis has more and more passed from differential equations, scattering theory, and probability to control theory and signal processing. This and the companion volume are geared toward a wide audience of readers, from graduate students to professional mathematicians. They develop an elementary approach to the subject while retaining an expert level that can be applied in advanced analysis and selected applications.
Author : Anonim
Publisher : Unknown
Page : 439 pages
File Size : 49,6 Mb
Release : 2002
Category : Control theory
ISBN : OCLC:874289944
Author : Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher : Unknown
Page : 479 pages
File Size : 55,9 Mb
Release : 2014-06-06
Category : MATHEMATICS
ISBN : 1470413191
One of two volumes, this text combines distinct topics of modern analysis and its applications: Hardy classes of holomorphic functions; spectral theory of Hankel and Toeplitz operators. Each topic has important implications for complex analysis.
Author : Nikolai K. Nikolski
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 51,9 Mb
Release : 2002
Category : Computers
ISBN : 9780821849330
One of two volumes, this text combines distinct topics of modern analysis and its applications: Hardy classes of holomorphic functions; spectral theory of Hankel and Toeplitz operators. Each topic has important implications for complex analysis.
Author : Joseph A. Ball,Vladimir Bolotnikov
Publisher : Cambridge University Press
Page : 439 pages
File Size : 49,9 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781316518991
This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.
Author : Kehe Zhu
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 40,8 Mb
Release : 2007
Category : Function spaces
ISBN : 9780821839652
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
Author : Marek Ptak
Publisher : Springer Nature
Page : 423 pages
File Size : 51,9 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9783031506130
Author : Barry Simon
Publisher : Springer Nature
Page : 445 pages
File Size : 45,6 Mb
Release : 2019-08-29
Category : Mathematics
ISBN : 9783030224226
This book provides an in depth discussion of Loewner’s theorem on the characterization of matrix monotone functions. The author refers to the book as a ‘love poem,’ one that highlights a unique mix of algebra and analysis and touches on numerous methods and results. The book details many different topics from analysis, operator theory and algebra, such as divided differences, convexity, positive definiteness, integral representations of function classes, Pick interpolation, rational approximation, orthogonal polynomials, continued fractions, and more. Most applications of Loewner’s theorem involve the easy half of the theorem. A great number of interesting techniques in analysis are the bases for a proof of the hard half. Centered on one theorem, eleven proofs are discussed, both for the study of their own approach to the proof and as a starting point for discussing a variety of tools in analysis. Historical background and inclusion of pictures of some of the main figures who have developed the subject, adds another depth of perspective. The presentation is suitable for detailed study, for quick review or reference to the various methods that are presented. The book is also suitable for independent study. The volume will be of interest to research mathematicians, physicists, and graduate students working in matrix theory and approximation, as well as to analysts and mathematical physicists.
Author : Javad Mashreghi, Emmanuel Fricain,William Ross
Publisher : American Mathematical Soc.
Page : 317 pages
File Size : 49,6 Mb
Release : 2015-04-23
Category : Banach spaces
ISBN : 9781470410452
This volume contains the proceedings of the CRM Workshop on Invariant Subspaces of the Shift Operator, held August 26-30, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The main theme of this volume is the invariant subspaces of the shift operator (or its adjoint) on certain function spaces, in particular, the Hardy space, Dirichlet space, and de Branges-Rovnyak spaces. These spaces, and the action of the shift operator on them, have turned out to be a precious tool in various questions in analysis such as function theory (Bieberbach conjecture, rigid functions, Schwarz-Pick inequalities), operator theory (invariant subspace problem, composition operator), and systems and control theory. Of particular interest is the Dirichlet space, which is one of the classical Hilbert spaces of holomorphic functions on the unit disk. From many points of view, the Dirichlet space is an interesting and challenging example of a function space. Though much is known about it, several important open problems remain, most notably the characterization of its zero sets and of its shift-invariant subspaces. This book is co-published with the Centre de Recherches Mathématiques.
Author : Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher : American Mathematical Society(RI)
Page : 0 pages
File Size : 44,5 Mb
Release : 2002
Category : Control theory
ISBN : 0821828762
Overall, this work combines together - in two volumes - four formally distinct topics of modern analysis and their applications: Hardy classes of holomorphic functions; spectral theory of Hankel and Toeplitz operators; function models for linear operators and free interpolations; and infinite-dimensional system theory and signal processing. This, the second volume, contains parts C and D of the whole.
Author : Andrew Knightly,Charles Li
Publisher : American Mathematical Soc.
Page : 392 pages
File Size : 40,9 Mb
Release : 2006
Category : Hecke operators
ISBN : 9780821837399
The Fourier coefficients of modular forms are of widespread interest as an important source of arithmetic information. In many cases, these coefficients can be recovered from explicit knowledge of the traces of Hecke operators. The original trace formula for Hecke operators was given by Selberg in 1956. Many improvements were made in subsequent years, notably by Eichler and Hijikata. This book provides a comprehensive modern treatment of the Eichler-Selberg/Hijikata trace formulafor the traces of Hecke operators on spaces of holomorphic cusp forms of weight $\mathtt{k >2$ for congruence subgroups of $\operatorname{SL 2(\mathbf{Z )$. The first half of the text brings together the background from number theory and representation theory required for the computation. Thisincludes detailed discussions of modular forms, Hecke operators, adeles and ideles, structure theory for $\operatorname{GL 2(\mathbf{A )$, strong approximation, integration on locally compact groups, the Poisson summation formula, adelic zeta functions, basic representation theory for locally compact groups, the unitary representations of $\operatorname{GL 2(\mathbf{R )$, and the connection between classical cusp forms and their adelic counterparts on $\operatorname{GL 2(\mathbf{A )$. Thesecond half begins with a full development of the geometric side of the Arthur-Selberg trace formula for the group $\operatorname{GL 2(\mathbf{A )$. This leads to an expression for the trace of a Hecke operator, which is then computed explicitly. The exposition is virtually self-contained, withcomplete references for the occasional use of auxiliary results. The book concludes with several applications of the final formula.
Author : Daniel Gorenstein,Richard Lyons,Ronald Solomon
Publisher : American Mathematical Soc.
Page : 467 pages
File Size : 54,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821827765
The classification of finite simple groups is a landmark result of modern mathematics. The original proof is spread over scores of articles by dozens of researchers. In this multivolume book, the authors are assembling the proof with explanations and references. It is a monumental task. The book, along with background from sections of the previous volumes, presents critical aspects of the classification. In four prior volumes (Surveys of Mathematical Monographs, Volumes 40.1, 40.2, 40.3, and 40.4), the authors began the proof of the classification theorem by establishing certain uniqueness and preuniqueness results. In this volume, they now begin the proof of a major theorem from the classification grid, namely Theorem ${\mathcal C 7$. The book is suitable for graduate students and researchers interested in group theory.
