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Some Points of Analysis and Their History
Lars Gårding, Lund University, Sweden
A co-publication of the AMS and Higher Education Press (Beijing).
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University Lecture Series
1997; 88 pp; softcover
Volume: 11
ISBN-10: 0-8218-0757-9
ISBN-13: 978-0-8218-0757-6
List Price: US$20
Member Price: US$16
Order Code: ULECT/11
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This book is a collection of small essays containing the history and the proofs of some important and interesting theorems of analysis and partial differential operators in this century. Most of the results in the book are associated with Swedish mathematicians. Also included are the Tarski-Seidenberg theorem and Wiener's classical results in harmonic analysis and a delightful essay on the impact of distributions in analysis. All mathematical points are fully explained, but some require a certain mature understanding from the reader. This book is a well-written, simple work that offers full mathematical treatment, along with insight and fresh points of view.

This book is copublished with Higher Education Press (Beijing) and is distributed worldwide, except in the People's Republic of China, by the American Mathematical Society.

Readership

Graduate students and research mathematicians.

Reviews

"... a leading mathematician considers 12 fundamental achievements in the history of analysis in the 20th century ... The mathematical details are well presented and the proofs to the main theorems are given."

-- Mathematical Reviews

"This lively book is a guided tour through some of the highlights of twentieth-century analysis ... can be recommended ... to a graduate student seminar ... one can pick up a number of the gems of analysis without having to mine whole seams."

-- Bulletin of the AMS

"L. Gårding presents 12 nicely presented survey articles on some concepts of classical analysis. This well presented booklet will be surely of interest to specialists in analysis and PDEs."

-- European Mathematical Society Newsletter

Table of Contents

  • Picard's great theorem
  • On Holmgren's uniqueness theorem
  • The Phragmén-Lindelöf principle
  • Nevanlinna theory
  • The Riesz-Thorin interpolation theorem
  • The mathematics of Wiener's Tauberian theorem
  • The Tarski-Seidenberg theorem
  • Intrinsic hyperbolicity
  • Hypoellipticity
  • Dirichlet's problem and Gårding's inequality
  • A sharp form of Gårding's inequality
  • The impact of distributions in analysis
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