Generalized Blaschke Products

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Generalized Blaschke Products

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Author : John Edison Brock
language : en
Publisher:
Release Date : 1950

Generalized Blaschke Products written by John Edison Brock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Functions categories.

Generalized Analytic Continuation

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Author : William T. Ross
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Generalized Analytic Continuation written by William T. Ross and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. The authors use the strong analogy with the summability of divergent series to motivate the subject. They are careful to cover the various types of continuations, attempting to unify them and suggesting some open questions. The book also addresses the role of such continuations in approximation theory and operator theory. The introductory overview provides a useful look at the history and context of the theory.

Hypercomplex Analysis New Perspectives And Applications

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Author : Swanhild Bernstein
language : en
Publisher: Springer
Release Date : 2014-10-10

Hypercomplex Analysis New Perspectives And Applications written by Swanhild Bernstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-10 with Mathematics categories.

Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.

Function Spaces In Modern Analysis

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Author : Krzysztof Jarosz
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-18

Function Spaces In Modern Analysis written by Krzysztof Jarosz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-18 with Mathematics categories.

This volume contains the proceedings of the Sixth Conference on Function Spaces, which was held from May 18-22, 2010, at Southern Illinois University at Edwardsville. 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), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.

The Dirichlet Space And Related Function Spaces

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Author : Nicola Arcozzi
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-03

The Dirichlet Space And Related Function Spaces written by Nicola Arcozzi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-03 with Mathematics categories.

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.

Function Theory

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Author : Eric T. Sawyer
language : en
Publisher: American Mathematical Soc.
Release Date :

Function Theory written by Eric T. Sawyer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

Quasiconformal Surgery In Holomorphic Dynamics

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Author : Bodil Branner
language : en
Publisher: Cambridge University Press
Release Date : 2014-01-23

Quasiconformal Surgery In Holomorphic Dynamics written by Bodil Branner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-23 with Mathematics categories.

A comprehensive introduction to quasiconformal surgery in holomorphic dynamics. Contains a wide variety of applications and illustrations.

Invariant Subspaces Of Hardy Classes On Infinitely Connected Open Surfaces

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Author : Charles W. Neville
language : en
Publisher: American Mathematical Soc.
Release Date : 1975

Invariant Subspaces Of Hardy Classes On Infinitely Connected Open Surfaces written by Charles W. Neville and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.

We generalize Beurling's theorem on the shift invariant subspaces of Hardy class H[superscript]2 of the unit disk to the Hardy classes of admissible Riemann surfaces. Essentially, an open Riemann surface is admissible if it admits enough bounded multiple valued analytic functions. The class of admissible surfaces contains many infinitely connected surfaces, and all finite surfaces, but does not contain all plane regions admitting sufficiently many bounded analytic functions to sseparatepoints. We generalize the ttheorem of A.H. Read and the Cauchy integral formula to the boundary values, on the Hayashi boundary, of functions in the Hardy classes of admissible surfaces.

Operators Of Class C 0 With Spectra In Multiply Connected Regions

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Author : Adele Zucchi
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Operators Of Class C 0 With Spectra In Multiply Connected Regions written by Adele Zucchi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

In the present paper the author studies the analogue of the class [italic capital]C0 within a class of operators having a functional calculus based on the algebra of bounded holomorphic functions in a finitely connected domain with an analytic boundary. The latter class consists of the operators having the closure of the domain as a spectral set and having no normal direct summands with spectra contained in the boundary of the domain. (If the domain is the disk the preceding class reduces to the class of completely nonunitary contractions.) The basic properties known for the case of the disk, including the model theory, are established. The extension, even the mere construction of the functional calculus, is not routine, in part because it is unknown whether the analogue of Sz.-Nagy's dilation theorem is true in the author's multiply connected setting.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathema tics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclo paedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977 - 1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivision has been used). The main requirement for these articles has been that they should give a reason ably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of pre cise theorems with detailed definitions and technical details on how to carry out proofs and con structions.