Introduction to Model Spaces and their Operators
Title | Introduction to Model Spaces and their Operators PDF eBook |
Author | Stephan Ramon Garcia |
Publisher | Cambridge University Press |
Total Pages | 339 |
Release | 2016-05-17 |
Genre | Mathematics |
ISBN | 1316390438 |
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.
Introduction to Model Spaces and their Operators
Title | Introduction to Model Spaces and their Operators PDF eBook |
Author | Stephan Ramon Garcia |
Publisher | Cambridge University Press |
Total Pages | 339 |
Release | 2016-05-17 |
Genre | Mathematics |
ISBN | 1107108748 |
A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.
Lectures on Analytic Function Spaces and their Applications
Title | Lectures on Analytic Function Spaces and their Applications PDF eBook |
Author | Javad Mashreghi |
Publisher | Springer Nature |
Total Pages | 426 |
Release | 2023-11-14 |
Genre | Mathematics |
ISBN | 3031335724 |
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.
Introduction to Operator Theory in Riesz Spaces
Title | Introduction to Operator Theory in Riesz Spaces PDF eBook |
Author | Adriaan C. Zaanen |
Publisher | Springer Science & Business Media |
Total Pages | 312 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642606377 |
Since the beginning of the thirties a considerable number of books on func tional analysis has been published. Among the first ones were those by M. H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text books. Therefore, authors of textbooks usually restrict themselves to normed spaces (or even to Hilbert space exclusively) and linear operators in these spaces. In more advanced texts Banach algebras and (or) topological vector spaces are sometimes included. It is only rarely, however, that the notion of order (partial order) is explicitly mentioned (even in more advanced exposi tions), although order structures occur in a natural manner in many examples (spaces of real continuous functions or spaces of measurable function~). This situation is somewhat surprising since there exist important and illuminating results for partially ordered vector spaces, in . particular for the case that the space is lattice ordered. Lattice ordered vector spaces are called vector lattices or Riesz spaces. The first results go back to F. Riesz (1929 and 1936), L. Kan torovitch (1935) and H. Freudenthal (1936).
Introduction to Operator Space Theory
Title | Introduction to Operator Space Theory PDF eBook |
Author | Gilles Pisier |
Publisher | Cambridge University Press |
Total Pages | 492 |
Release | 2003-08-25 |
Genre | Mathematics |
ISBN | 9780521811651 |
An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
An Introduction to Models and Decompositions in Operator Theory
Title | An Introduction to Models and Decompositions in Operator Theory PDF eBook |
Author | Carlos S. Kubrusly |
Publisher | Springer Science & Business Media |
Total Pages | 141 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461219981 |
By a Hilbert-space operator we mean a bounded linear transformation be tween separable complex Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active research topics in operator theory over the past three decades. The main motivation behind them is the in variant subspace problem: does every Hilbert-space operator have a nontrivial invariant subspace? This is perhaps the most celebrated open question in op erator theory. Its relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral Theorem), as well as operators on finite dimensional Hilbert spaces (witness: canonical Jordan form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form) is important enough an achievement to dismiss any further justification, then the search for nontrivial invariant subspaces is a natural one; and a recalcitrant one at that. Subnormal operators have nontrivial invariant subspaces (extending the normal branch), as well as compact operators (extending the finite-dimensional branch), but the question remains unanswered even for equally simple (i. e. simple to define) particular classes of Hilbert-space operators (examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has certainly not been a failure at all, even though far from being settled. The search for nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory, among them, those concerning decompositions and models for Hilbert-space operators. This book contains nine chapters.
An Introduction to Operators on the Hardy-Hilbert Space
Title | An Introduction to Operators on the Hardy-Hilbert Space PDF eBook |
Author | Ruben A. Martinez-Avendano |
Publisher | Springer Science & Business Media |
Total Pages | 230 |
Release | 2007-03-12 |
Genre | Mathematics |
ISBN | 0387485783 |
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.