**University Lecture Series**

Volume: 11;
1997;
88 pp;
Softcover

MSC: Primary 01;
Secondary 30; 35; 42; 46

**Print ISBN: 978-0-8218-0757-6
Product Code: ULECT/11**

List Price: $23.00

AMS Member Price: $18.40

MAA Member Price: $20.70

**Electronic ISBN: 978-1-4704-2160-1
Product Code: ULECT/11.E**

List Price: $21.00

AMS Member Price: $16.80

MAA Member Price: $18.90

# Some Points of Analysis and Their History

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*Lars Gårding*

A co-publication of the AMS and Higher Education Press (Beijing)

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.

#### Readership

Graduate students and research mathematicians.

#### Reviews & Endorsements

… 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

# Table of Contents

## Some Points of Analysis and Their History

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Author's preface vii8 free
- 1. Picard's great theorem 110 free
- 2. On Holmgren's uniqueness theorem 918
- 3. The Phragmén-Lindelöf principle 1524
- 4. Nevanlinna theory 2332
- 5. The Riesz-Thorin interpolation theorem 3140
- 6. The Mathematics of Wiener's Tauberian theorem 3746
- 7. The Tarski-Seidenberg theorem 4958
- 8. Intrinsic hyperbolicity 5564
- 9. Hypoellipticity 6170
- 10. Dirichlet's problem and Gärding's inequality 6574
- 11. A sharp form of Gärding's inequality 7180
- 12. The impact of distributions in analysis 7786
- Back Cover Cover198