有界解析函數(shù)

前言

This edition of Bounded Analytic Functions is the same as the first edition exceptfor the corrections of several mathematical and typographical errors. I thank themany colleagues and students who have pointed out errors in the first edition.These include S. Axler, C. Bishop, A. Carbery, K. Dyakonov, J. Handy, V. Havin, H.Hunziker, E Koosis, D. Lubinsky, D. Marshall, R. Mortini, A. Nicolau, M. O'Neill,W. Rudin, D. Sarason, D. Suarez, C. Sundberg, C. Thiele, S. Treil, L Uriarte-Tuero,J. Vaisali, N. Varopoulos, and L. Ward.I had planned to prepare a second edition with an updated bibliography and anappendix on results new in the field since 1981, but that work has been postponed fortoo long. In the meantime several excellent related books have appeared, includingM. Andersson, Topics in Complex Analysis; G. David and S. Semmes, SingularIntegrals and Rectifiable Sets in Rn and Analysis of and on Uniformly Rectifi-able Sets; S. Fischer, Function theory on planar domains; P. Koosis, Introductionto Hp spaces, Second edition; N. Nikolski, Operators, Functions, and Systems;K. Seip, Interpolation and Sampling in Spaces of Analytic Functions; and B. Simon,Orthogonal Polynomials on the Unit Circle.

內(nèi)容概要

本書旨在介紹一維Hardy空間理論，強(qiáng)調(diào)近幾十年來該領(lǐng)域的重大發(fā)展。書中的后七章都致力于最新結(jié)果。講述Hardy空間理論旨在闡述實分析、復(fù)分析和抽象分析的相互關(guān)系，并將其延伸到歐幾里得空間。為了幫助讀者更好地學(xué)習(xí)該教材，每章的結(jié)尾都有注、練習(xí)和進(jìn)一步結(jié)果。前幾節(jié)講述簡短的歷史評論以引導(dǎo)讀者了解本書的原始資料。內(nèi)容安排結(jié)構(gòu)緊湊合理、文筆優(yōu)美，證明詳盡。本書影響了許多早期杰出的分析學(xué)家，培育了一代有復(fù)分析和函數(shù)代數(shù)背景的數(shù)學(xué)家，對今天該領(lǐng)域的學(xué)者也是一本非常經(jīng)典的參考書。本書被許多美國大學(xué)的作為研究生教材。目次：預(yù)備知識；Hp空間；共軛函數(shù)；附加問題；一致代數(shù)；有界平均振動；插值序列；Corona結(jié)構(gòu)；Douglas代數(shù)；插值序列和最大理想。    讀者對象：數(shù)學(xué)專業(yè)的高年級本科生、研究生和分析領(lǐng)域相關(guān)的讀者。

書籍目錄

Preface List of Symbols Ⅰ.PRELIMINARIES 　1.Schwarz's Lemma 　2.Pick's Theorem 　3.Poisson Integrals 　4.Hardy-Littlewood Maximal Function 　5.Nontangential Maximal Function and Fatou's Theorem 　6.Subharmonic Functions 　Notes 　Exercises and Further Results Ⅱ.Hp SPACES 　1.Definitions 　2.Blaschke Products 　3.Maximal Functions and Boundary Values ……Ⅲ.CONJUGATE FUNCITONSⅣ.SOME EXTREMAL PROBLEMSⅤ.SOME UNIFORM ALGEBRAⅥ.BOUNDED MEAN OSCILLATIONⅦ.INTERPOLATING SEQUENCESⅧ.THE CORONA COMSTRUCTIONⅨ.DOUGLAS ALGEBRASⅩ.XINTERPOLATING SEQUENCES AND MAXIMAL IDEALSBIBLIOGRAPHYINDEX

章節(jié)摘錄

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《有界解析函數(shù)(修訂版)(英文版)》是由世界圖書出版公司出版的。

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