Lecture notes in mathematics
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Lecture notes in mathematics
Lecture Notes in MathematicsEdited by A. Dold and B. EckmannSeries: California Institute of Technology, PasadenaAdviser: c. R, DePrima593Klaus BarbeyH Lecture notes in mathematics Heinz KonigAbstract Analytic Function Theory and Hardy AlgebrasSpringer-VerlagBerlin • Heidelberg • New York 1977AuthorsKlaus Barbey Fachbereich Mathematik Umversitat Regensburg UniversitătsstraBe 31 8400 Regensburg/BRDHeinz KonigFachbereich Mathomatik Universităt des Saarlandes 6600 Saarbrucken/BRD Lecture notes in mathematics AMS Subject Classifications (1970): 46 J10. 46J15ISBN 3-540-08252-2 Springer-Verlag Berlin • Heidelberg ■ New York ISBN 0-387-08252-2 Springer-VerlagLecture notes in mathematics
New York ■ Heidelberg • BerlinThis work is subject to copyright. All rights are reserved, whether the whoie or part of the material is concerned, specLecture Notes in MathematicsEdited by A. Dold and B. EckmannSeries: California Institute of Technology, PasadenaAdviser: c. R, DePrima593Klaus BarbeyH Lecture notes in mathematics n data banks.Under § 54 of the German Copyright Law where copies are made for other than private use. a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.© by Springer-Veriag Berlin • Heidelberg 1977Printed in GermanyPrinting and binding: Beltz O Lecture notes in mathematics ffsetdruck, Hemsbach/Bergstr.2141/3140-543210PrefaceThe present work wants to be the systematic presentation of a functional-analytic theory. It is anLecture notes in mathematics
abstract version of those parts of classical analytic function theory which can be circumscribed by boundary value theory and Hardy spaces The fascinLecture Notes in MathematicsEdited by A. Dold and B. EckmannSeries: California Institute of Technology, PasadenaAdviser: c. R, DePrima593Klaus BarbeyH Lecture notes in mathematics ory the tools of which arc standard real-analytic methods such as elementary functional analysis and measure theory. The abstract theory started about twenty years ago in papers of Arens and Singer, Gleason, Kelson and Lowdenslager, Bochner, Bishop, Wermer,... and went through several steps of abstr Lecture notes in mathematics action (Dirichlet algebras, logmodular algebras,...). It never ceased to radiate back and illuminate the concrete classical theory. We present the ultLecture notes in mathematics
imate step of abstraction which hasbeen under work for aboutten years.The central concept is theabstract Hardyalgebra situation. Itiscomprehensive as Lecture Notes in MathematicsEdited by A. Dold and B. EckmannSeries: California Institute of Technology, PasadenaAdviser: c. R, DePrima593Klaus BarbeyH Lecture notes in mathematics pters IV-IX. The abstract Hardy algebra situation can be looked upon as a local section of the abstract function algebra situation. To achieve the localization is the main business of the abstract F.and M.Riesz theorem and of the resultant Gleason part decomposition procedure. These are central them Lecture notes in mathematics es in Chapters II-III devoted to the abstract function algebra situation. Chapter I presents the concrete unit disk situation in such a spirit as to pLecture notes in mathematics
repare the abstract concepts. Chapter X is devoted to standard applications of the abstract theory to polynomial and rational approximation in Lho comLecture Notes in MathematicsEdited by A. Dold and B. EckmannSeries: California Institute of Technology, PasadenaAdviser: c. R, DePrima593Klaus BarbeyH Lecture notes in mathematics t comprehensive of which is GAMELIN [1969], the present work contains numerous new results. In concepts and systematization it is shaped after the work of Kõnỉg. Most of the chapters contain substantial new material. A prime point is the systematic use of the associated algebra p/. The most importan Lecture notes in mathematics t individual new result is perhaps the approximation theorem VI.4.1. Let US also quote Section VI.5 on the Marcel Riesz estimation for the abstract coLecture notes in mathematics
njugation after fundamental results of Pichorides in the unit disk situation. For more details we refer to the Introductions and Notes to the individuLecture Notes in MathematicsEdited by A. Dold and B. EckmannSeries: California Institute of Technology, PasadenaAdviser: c. R, DePrima593Klaus BarbeyH Lecture notes in mathematics at the California Institute of Technology in Pasadena/California, and which in part had been distributed in a provisional form. He wants to express his warmest thanks to Wim Luxemburg and Charles DePrima who were his hosts in those days, and likewise to Gunter Lumer to whom he owes the participation Lecture notes in mathematics in the Function Algebra Seminar at the University of Washington in Seat..tle/Washington in 1970. Above all he sends his deepest thanks to Galen SeeveLecture notes in mathematics
r and to KÔ2Ô Yabuta for most valuable and pleasant cooperation, and he wants to include his former student Klaus Barbey who started to participate wiLecture Notes in MathematicsEdited by A. Dold and B. EckmannSeries: California Institute of Technology, PasadenaAdviser: c. R, DePrima593Klaus BarbeyH Lecture notes in mathematics re thanks to Michael Neumann for his active interest and valuable work in connection with a common seminar, to Ulla Faust and Gisela Schirmbeck who typed the final text with impressive care and thoughtfulness, to Horst Loch who read most of the proofs with distinctive care, and to Karla May and Gerd Lecture notes in mathematics Rode for their kind assistance.ContentsChapter I. Boundary Value Theory for Harmonic and Holomorphic Functions in the Unit Disk ... .................Lecture notes in mathematics
....................1.Harmonic Functions ............................................. 1Lecture Notes in MathematicsEdited by A. Dold and B. EckmannSeries: California Institute of Technology, PasadenaAdviser: c. R, DePrima593Klaus BarbeyHLecture Notes in MathematicsEdited by A. Dold and B. EckmannSeries: California Institute of Technology, PasadenaAdviser: c. R, DePrima593Klaus BarbeyHGọi ngay
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