有界解析函数

出版时间：2010-1  出版社：世界图书出版公司  作者：加耐特  页数：459  

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.

内容概要

本书旨在介绍一维Hardy空间理论，强调近几十年来该领域的重大发展。书中的后七章都致力于最新结果。讲述Hardy空间理论旨在阐述实分析、复分析和抽象分析的相互关系，并将其延伸到欧几里得空间。为了帮助读者更好地学习该教材，每章的结尾都有注、练习和进一步结果。前几节讲述简短的历史评论以引导读者了解本书的原始资料。内容安排结构紧凑合理、文笔优美，证明详尽。本书影响了许多早期杰出的分析学家，培育了一代有复分析和函数代数背景的数学家，对今天该领域的学者也是一本非常经典的参考书。本书被许多美国大学的作为研究生教材。目次：预备知识；Hp空间；共轭函数；附加问题；一致代数；有界平均振动；插值序列；Corona结构；Douglas代数；插值序列和最大理想。    读者对象：数学专业的高年级本科生、研究生和分析领域相关的读者。

书籍目录

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

章节摘录

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《有界解析函数(修订版)(英文版)》是由世界图书出版公司出版的。

用户评论 (总计3条)

•   书的质量不错，感觉还行
•   这本书真难买，还好有卓越
•   这本书是经典教材， 很好， 就是有点难， 但绝对是复分析方面的经典教材