Softcover ISBN:  9780821807576 
Product Code:  ULECT/11 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470421601 
Product Code:  ULECT/11.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821807576 
eBook: ISBN:  9781470421601 
Product Code:  ULECT/11.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 
Softcover ISBN:  9780821807576 
Product Code:  ULECT/11 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470421601 
Product Code:  ULECT/11.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821807576 
eBook ISBN:  9781470421601 
Product Code:  ULECT/11.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 11; 1997; 88 ppMSC: Primary 01; Secondary 30; 35; 42; 46
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 TarskiSeidenberg 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 wellwritten, 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.
ReadershipGraduate students and research mathematicians.

Table of Contents

Chapters

Chapter 1. Picard’s great theorem

Chapter 2. On Holmgren’s uniqueness theorem

Chapter 3. The PhragménLindelöf principle

Chapter 4. Nevanlinna theory

Chapter 5. The RieszThorin interpolation theorem

Chapter 6. The mathematics of Wiener’s Tauberian theorem

Chapter 7. The TarskiSeidenberg theorem

Chapter 8. Intrinsic hyperbolicity

Chapter 9. Hypoellipticity

Chapter 10. Dirichlet’s problem and Gårding’s inequality

Chapter 11. A sharp form of Gårding’s inequality

Chapter 12. The impact of distributions in analysis


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 twentiethcentury 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


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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 TarskiSeidenberg 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 wellwritten, 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.
Graduate students and research mathematicians.

Chapters

Chapter 1. Picard’s great theorem

Chapter 2. On Holmgren’s uniqueness theorem

Chapter 3. The PhragménLindelöf principle

Chapter 4. Nevanlinna theory

Chapter 5. The RieszThorin interpolation theorem

Chapter 6. The mathematics of Wiener’s Tauberian theorem

Chapter 7. The TarskiSeidenberg theorem

Chapter 8. Intrinsic hyperbolicity

Chapter 9. Hypoellipticity

Chapter 10. Dirichlet’s problem and Gårding’s inequality

Chapter 11. A sharp form of Gårding’s inequality

Chapter 12. The impact of distributions in analysis

... 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 twentiethcentury 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