Uniform Algebras And Jensen Measures
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| Author | : Theodore W. Gamelin |
| Publisher | : Cambridge University Press |
| Total Pages | : 173 |
| Release | : 1978 |
| Genre | : Mathematics |
| ISBN | : 052122280X |
These lecture notes are devoted to an area of current research interest that bridges functional analysis and function theory. The unifying theme is the notion of subharmonicity with respect to a uniform algebra. The topics covered include the rudiments of Choquet theory, various classes of representing measures, the duality between abstract sub-harmonic functions and Jensen measures, applications to problems of approximation of plurisubharmonic functions of several complex variables, and Cole's theory of estimates for conjugate functions. Many of the results are published here for the first time in monograph form.
| Author | : Theodore W. Gamelin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 292 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 9780821840498 |
From the Preface: ``The functional-analytic approach to uniform algebras is inextricably interwoven with the theory of analytic functions ... [T]he concepts and techniques introduced to deal with these problems [of uniform algebras], such as ``peak points'' and ``parts,'' provide new insights into the classical theory of approximation by analytic functions. In some cases, elegant proofs of old results are obtained by abstract methods. The new concepts also lead to new problems in classical function theory, which serve to enliven and refresh that subject. In short, the relation between functional analysis and the analytic theory is both fascinating and complex, and it serves to enrich and deepen each of the respective disciplines.'' This volume includes a Bibliography, List of Special Symbols, and an Index. Each of the chapters is followed by notes and numerous exercises.
| Author | : Allan M. Sinclair |
| Publisher | : Cambridge University Press |
| Total Pages | : 153 |
| Release | : 1982-06-17 |
| Genre | : Mathematics |
| ISBN | : 0521285984 |
In these notes the abstract theory of analytic one-parameter semigroups in Banach algebras is discussed, with the Gaussian, Poisson and fractional integral semigroups in convolution Banach algebras serving as motivating examples. Such semigroups are constructed in a Banach algebra with a bounded approximate identity. Growth restrictions on the semigroup are linked to the structure of the underlying Banach algebra. The Hille-Yosida Theorem and a result of J. Esterle's on the nilpotency of semigroups are proved in detail. The lecture notes are an expanded version of lectures given by the author at the University of Edinburgh in 1980 and can be used as a text for a graduate course in functional analysis.
| Author | : R. Y. Sharp |
| Publisher | : Cambridge University Press |
| Total Pages | : 265 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : 0521271258 |
This book is concerned with the research conducted in the late 1970s and early 1980s in the theory of commutative Neotherian rings. It consists of articles by invited speakers at the Symposium of Commutative Algebra held at the University of Durham in July 1981; these articles are all based on lectures delivered at the Symposium. The purpose of this book is to provide a record of at least some aspects of the Symposium, which several of the world leaders in the field attended. Several articles are included which provide surveys, incorporating historical perspective, details of progress made and indications of possible future lines of investigation. The book will be of interest to scholars of commutative and local algebra.
| Author | : P. Landrock |
| Publisher | : Cambridge University Press |
| Total Pages | : 287 |
| Release | : 1983-12-29 |
| Genre | : Mathematics |
| ISBN | : 0521274877 |
This book is concerned with the structure of group algebras of finite groups over fields of characteristic [lowercase italic]p dividing the order of the group, or closely related rings such as rings of algebraic integers and in particular their [lowercase italic]p-adic completions, as well as modules and homomorphisms between them, or such group algebras. Our principal aim has been to present some of the more recent ideas which have enriched and improved this theory. This text is not restricted to particular methods, be they ring theoretic or character theoretic, while presenting approaches or proofs which are distinguished by being fast, elegant, illuminating, with potential for further advancement, or all of these at the same time. This text hopes to attract non-specialists, perhaps algebraic topologists and group theorists who might use the tools of modular representations more frequently.
| Author | : John Garnett |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 471 |
| Release | : 2007-04-05 |
| Genre | : Mathematics |
| ISBN | : 0387497633 |
This book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. While paying proper attention to each of the three aspects, the author has underscored the effectiveness of the methods coming from real analysis, many of them developed as part of a program to extend the theory to Euclidean spaces, where the complex methods are not available.
| Author | : N. Petridis |
| Publisher | : Springer |
| Total Pages | : 222 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540386327 |
In recent years there has been a tremendous growth in psychology as a field of study and in the number of students of clinical psychology in particular. The latter is partly due to the proliferation of professional schools of psychology that are devoted to practitioner-oriented degrees, rather than the traditional research-oriented course of study. Whatever school students emerge from, however, they are obliged to demonstrate proficiency in providing clinical services. This multi-volume handbook, is devoted to describing the core competency areas in providing psychological services which is relevant to practitioners as well as clinical researchers. As such, it covers assessment and conceptualization of cases, the application of evidence-based methods, supervision, consultation, cross-cultural factors, and ethics. The Handbook comprises three volumes with contributions by experts in each area. The goal is to provide detailed descriptions of competence levels and describe the developmental trajectory required to reach the highest of these levels. Each chapter in Volume I will follow a similar format including an overview, basic competencies, and expert competencies. This will facilitate easy comparison across chapters. All will be illustrated with case examples. Subsequent volumes will have a similarly structured format that will include maintenance factors, mechanisms of change, evidence-based treatment approaches, and a focus on the transition from basic skills to expert functioning. It is expected that the systematic presentation of skills will provide a gold standard against which to measure individual performance and in this regard will be valuable to students, instructors, and credentialing bodies.
| Author | : Oscar Blasco |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 266 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821852752 |
This book contains the lecture notes as well as some invited papers presented at the Third Winter School in Complex Analysis, Operator Theory and Applications held February 2-5, 2010, in Valencia, Spain. The book is divided into two parts. The first is an extended self-contained version of the mini-courses taught at the School. The papers in this first part are: Notes on real analytic functions and classical operators, by Pawel Domanski; Shining a Hilbertian lamp on the bidisk, by John E. McCarthy; Selected problems in perturbation theory, by Vladimir V. Peller; and Composition operators on Hardy-Orlicz spaces, by Luis Rodriguez-Piazza. The second part consists of several research papers on recent advances in the area and some survey articles of an expository character. The articles in this second part are: Remarks on weighted mixed norm spaces, by O. Blasco; Interpolation subspaces of $L^1$ of a vector measure and norm inequalities for the integration operator, by J.M. Calabuig, J. Rodriguez, and E.A. Sanchez-Perez; On the spectra of algebras of analytic functions, by D. Carando, D. Garcia, M. Maestre, and P. Sevilla-Peris; Holomorphic self-maps of the disk intertwining two linear fractional maps, by M.D. Contreras, S. Diaz-Madrigal, M.J. Martin, and D. Vukotic; ABC-type estimates via Garsia-type norms, by K.M. Dyakonov; and Volterra type operators on Bergman spaces with exponential weights, by J. Pau and J.A. Pelaez. The topics selected for the mini-courses cover several aspects of complex analysis and operator theory that play important roles in understanding connections between different areas that are considered in fashion these days. This part is aimed at graduate students and young researchers. The courses are self-contained, focusing on those aspects that are basic and that can lead the readers to a quick understanding of the theories presented in each topic. They start with the classical results and reach a selection of open problems in each case. The research and survey articles are aimed at young researchers in the area, as well as post-doc and senior researchers interested in complex analysis and operator theory. This book is published in cooperation with Real Sociedad Matematica Espanola.
| Author | : Stephen D. Fisher |
| Publisher | : Courier Corporation |
| Total Pages | : 292 |
| Release | : 2014-06-10 |
| Genre | : Mathematics |
| ISBN | : 0486151107 |
A high-level treatment of complex analysis, this text focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The first chapter and parts of Chapters 2 and 3 offer background material, all of it classical and important in its own right. The remainder of the text presents results in complex analysis from the far, middle, and recent past, all selected for their interest and merit as substantive mathematics. Suitable for upper-level undergraduates and graduate students, this text is accessible to anyone with a background in complex and functional analysis. Author Stephen D. Fisher, a professor of mathematics at Northwestern University, elaborates upon and extends results with a set of exercises at the end of each chapter.
| Author | : Barry Simon |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 769 |
| Release | : 2015-12-04 |
| Genre | : Mathematics |
| ISBN | : 1470411032 |
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 4 focuses on operator theory, especially on a Hilbert space. Central topics are the spectral theorem, the theory of trace class and Fredholm determinants, and the study of unbounded self-adjoint operators. There is also an introduction to the theory of orthogonal polynomials and a long chapter on Banach algebras, including the commutative and non-commutative Gel'fand-Naimark theorems and Fourier analysis on general locally compact abelian groups.
