Pick Interpolation And Hilbert Function Spaces

Author : Jim Agler
Publisher : American Mathematical Society
ISBN 13 : 1470468557
Total Pages : 330 pages
Book Rating : 4.52/5 ( download)

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Download or read book Pick Interpolation and Hilbert Function Spaces written by Jim Agler and published by American Mathematical Society. This book was released on 2023-02-22 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.

Author : Michael T. Jury
Publisher :
ISBN 13 :
Total Pages : 134 pages
Book Rating : 4.59/5 ( download)

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Download or read book Matrix Products and Interpolation Problems in Hilbert Function Spaces written by Michael T. Jury and published by . This book was released on 2002 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jim Agler
Publisher : Cambridge University Press
ISBN 13 : 1108485448
Total Pages : 393 pages
Book Rating : 4.49/5 ( download)

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Download or read book Operator Analysis written by Jim Agler and published by Cambridge University Press. This book was released on 2020-03-26 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.

Author : Michael Peter Hartz
Publisher :
ISBN 13 :
Total Pages : 175 pages
Book Rating : 4.33/5 ( download)

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Download or read book Nevanlinna-pick Spaces and Dilations written by Michael Peter Hartz and published by . This book was released on 2016 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The majority of this thesis is devoted to the study of Nevanlinna-Pick spaces and their multiplier algebras. These spaces are Hilbert function spaces in which a version of the Nevanlinna-Pick interpolation theorem from complex analysis holds. Their multiplier algebras occupy an important place at the interface between operator algebras, operator theory and complex analysis. Over the last few years, the classification problem for these algebras has attracted considerable attention. These investigations were pioneered by Davidson, Ramsey and Shalit, who used a theorem of Agler and McCarthy to identify a given multiplier algebra with the restriction of the multiplier algebra of the universal Nevanlinna-Pick space, namely the Drury-Arveson space, to an analytic variety in a complex ball. In this thesis, the classification problem is studied from three different angles. In Chapter 3, we investigate multiplier algebras associated to embedded discs in a complex ball. In particular, we exhibit uncountably many embedded discs which are biholomorphic in a strong sense, but whose multiplier algebras are not isomorphic. Motivated by these issues, we use in Chapter 4 a different approach to the classification problem. Thus, we study the spaces and their multiplier algebras directly without making use of the existence of a universal Nevanlinna-Pick space. This allows us to completely classify the multiplier algebras of a special class of spaces on homogeneous varieties. In Chapter 5, we investigate the complexity of this classification problem from the point of view of Borel complexity theory. In Chapter 6, we show that the Hardy space on the unit disc is essentially the only Nevanlinna-Pick space whose multiplication operators are all hyponormal. The last part of this thesis is concerned with dilations and von Neumann's inequality. It has been known since the seventies that there are three commuting contractions which do not satisfy von Neumann's inequality. In Chapter 7, we show that every tuple of commuting contractions which forms a multivariable weighted shift dilates to a tuple of commuting unitaries and hence satisfies von Neumann's inequality, thereby providing a positive answer to a question of Shields and Lubin from 1974.

Author : Nicola Arcozzi
Publisher : American Mathematical Soc.
ISBN 13 : 1470450828
Total Pages : 536 pages
Book Rating : 4.23/5 ( download)

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Download or read book The Dirichlet Space and Related Function Spaces written by Nicola Arcozzi and published by American Mathematical Soc.. This book was released on 2019-09-03 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
ISBN 13 : 0821840614
Total Pages : 402 pages
Book Rating : 4.10/5 ( download)

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Download or read book Function Spaces written by Krzysztof Jarosz and published by American Mathematical Soc.. This book was released on 2007 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.

Author : Alexandru Aleman
Publisher : Springer
ISBN 13 : 3030146405
Total Pages : 281 pages
Book Rating : 4.05/5 ( download)

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Download or read book Analysis of Operators on Function Spaces written by Alexandru Aleman and published by Springer. This book was released on 2019-05-30 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.

Author : Kristian Seip
Publisher : American Mathematical Soc.
ISBN 13 : 0821835548
Total Pages : 153 pages
Book Rating : 4.48/5 ( download)

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Download or read book Interpolation and Sampling in Spaces of Analytic Functions written by Kristian Seip and published by American Mathematical Soc.. This book was released on 2004 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's interpolation theorem, an

Author : Javad Mashreghi
Publisher : Springer Nature
ISBN 13 : 3031335724
Total Pages : 426 pages
Book Rating : 4.23/5 ( download)

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Download or read book Lectures on Analytic Function Spaces and their Applications written by Javad Mashreghi and published by Springer Nature. This book was released on 2023-11-14 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins—the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)—have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. More explicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.

Author : Sheldon Axler
Publisher : Springer Science & Business Media
ISBN 13 : 3034603479
Total Pages : 360 pages
Book Rating : 4.78/5 ( download)

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Download or read book A Glimpse at Hilbert Space Operators written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2011-04-13 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Richard Halmos, who lived a life of unbounded devotion to mathematics and to the mathematical community, died at the age of 90 on October 2, 2006. This volume is a memorial to Paul by operator theorists he inspired. Paul’sinitial research,beginning with his 1938Ph.D. thesis at the University of Illinois under Joseph Doob, was in probability, ergodic theory, and measure theory. A shift occurred in the 1950s when Paul’s interest in foundations led him to invent a subject he termed algebraic logic, resulting in a succession of papers on that subject appearing between 1954 and 1961, and the book Algebraic Logic, published in 1962. Paul’s ?rst two papers in pure operator theory appeared in 1950. After 1960 Paul’s research focused on Hilbert space operators, a subject he viewed as enc- passing ?nite-dimensional linear algebra. Beyond his research, Paul contributed to mathematics and to its community in manifold ways: as a renowned expositor, as an innovative teacher, as a tireless editor, and through unstinting service to the American Mathematical Society and to the Mathematical Association of America. Much of Paul’s in?uence ?owed at a personal level. Paul had a genuine, uncalculating interest in people; he developed an enormous number of friendships over the years, both with mathematicians and with nonmathematicians. Many of his mathematical friends, including the editors ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul’sknee, learned from his advice and his example what it means to be a mathematician.