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20. Pattern recognition and statistical learning theory (the theory of support vector machines). See [40], [58]. In this last volume we refer in particular to the papers [63] and [64]. Since this topic is maybe less known to the operator theory community we mention that the support vector method is a general approach to function estimation problems. See [63, p. 26]. We note that the above list and the given references are by no way exhaustive. We refer to the first section of the paper of S. Saitoh in the present volume for another (and mainly different) list of topics where reproducing kernel spaces appear. Quite often a given question is best understood in a reproducing kernel Hilbert space (for instance when using Cauchy's formula in the Hardy space H) 2 and one finds oneself as Mr Jourdain of Moliere'Bourgeois Gentilhomme speaking Prose without knowing it [48, p. 51]: Par ma foil il y a plus de quarante ans que je dis de la prose sans que l j'en susse rien.

This volume contains twenty-one solicited articles by speakers at the IWOTA 2009 workshop, ranging from expository surveys to original research papers, each carefully refereed. The contributions reflect recent developments in operator theory and its applications. Consistent with the topics of recent IWOTA meetings, IWOTA 2009 was designed as a comprehensive, inclusive conference covering all aspects of theoretical and applied operator theory, ranging from classical analysis, differential and integral equations, complex and harmonic analysis to mathematical physics, mathematical systems and control theory, signal processing and numerical analysis. The conference brought together international experts for a week-long stay at Hotel Real de Minas, in an atmosphere conducive to fruitful professional interactions. These Proceedings reflect the high quality of the papers presented at the conference.

This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory. The papers, written by leading researchers in the field, relate to hypercomplex analysis, Schur analysis and de Branges spaces, new aspects of classical function theory, and infinite dimensional analysis. Signal processing constitutes a strong presence in several of the papers.A second volume in this series of conferences, this book will appeal to mathematicians interested in learning about new fields of development in function theory.

This book gathers contributions written by Daniel Alpay's friends and collaborators. Several of the papers were presented at the International Conference on Complex Analysis and Operator Theory held in honor of Professor Alpay's 60th birthday at Chapman University in November 2016. The main topics covered are complex analysis, operator theory and other areas of mathematics close to Alpay's primary research interests. The book is recommended for mathematicians from the graduate level on, working in various areas of mathematical analysis, operator theory, infinite dimensional analysis, linear systems, and stochastic processes.

Operator theory, system theory, scattering theory, and the theory of analytic functions of one complex variable are deeply related topics, and the relationships between these theories are well understood. When one leaves the setting of one operator and considers several operators, the situation is much more involved. There is no longer a single underlying theory, but rather different theories, some of them loosely connected and some not connected at all. These various theories, which one could call'multidimensional operator theory', are topics of active and intensive research.The present volume contains a selection of papers in multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations.The volume will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoreticalphysicists.

This book is about function spaces aspects of polyanalytic functions, a topic that has gained a lot of attention in the past decades. This book fills a gap in literature and is written by a leading researcher in the field. Rather than studying polyanalytic functions from a complex analysis point of view, it considers the (Lie)-algebraic part of the theory. Several generalizations are offered. The presented theory has many applications, including to quantum physics. An extensive introduction to the topic is provided, making the book accessible to specialists and newcomers alike.

This volume contains the proceedings of the International Workshop on Operator Theory and Applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the conference were!> Factorization Theory;!> Factorization and Integrable Systems;!> Operator Theoretical Methods in Diffraction Theory;!> Algebraic Techniques in Operator Theory;!> Applications to Mathematical Physics and Related Topics. A total of 94 colleagues from 21 countries participated in the conference. The major part of participants came from Portugal (32), Germany (17), Israel (6), Mexico (6), the Netherlands (5), USA (4) and Austria (4). The others were from Ukraine, Venezuela (3 each), Spain, Sweden (2 each), Algeria, Australia, Belorussia, France, Georgia, Italy, Japan, Kuwait, Russia and Turkey (one of each country). It was the 12th meeting in the framework of the IWOTA conferences which started in 1981 on an initiative of Professors 1. Gohberg (Tel Aviv) and J. W. Helton (San Diego). Up to now, it was the largest conference in the field of Operator Theory in Portugal.

Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups. In this essentially self-contained work, the basic ideas underlying the concept of Dirac operators are explored. Starting with Clifford algebras and the fundamentals of differential geometry, the text focuses on two main properties, namely, conformal invariance, which determines the local behavior of the operator, and the unique continuation property dominating its global behavior. Spin groups and spinor bundles are covered, as well as the relations with their classical counterparts, orthogonal groups and Clifford bundles. The chapters on Clifford algebras and the fundamentals of differential geometry can be used as an introduction to the above topics, and are suitable for senior undergraduate and graduate students. The other chapters are also accessible at this level so that this text requires very little previous knowledge of the domains covered. The reader will benefit, however, from some knowledge of complex analysis, which gives the simplest example of a Dirac operator. More advanced readers---mathematical physicists, physicists and mathematicians from diverse areas---will appreciate the fresh approach to the theory as well as the new results on boundary value theory.

The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.​

This volume is dedicated to Bill Helton on the occasion of his sixty fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty odd years. These include interpolation, Szegö limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization.The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied mathematics and engineering, as well as a source book for seminars.

This book presents holomorphic operator functions of a single variable and applications, which are focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables.

This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.