The Logarithmic Integral: Volume 1

Self-contained study of real and complex analysis bringing together many separate parts of this subject.

Paul Koosis (Author)

9780521596725, Cambridge University Press

Paperback, published 29 October 1998

628 pages, 156 b/w illus.
23 x 15.5 x 3.1 cm, 0.834 kg

'The book is well written and can be recommended to anyone interested in real and complex analysis.' EMS

The theme of this unique work, the logarithmic integral, lies athwart much of twentieth century analysis. It is a thread connecting many apparently separate parts of the subject, and so is a natural point at which to begin a serious study of real and complex analysis. Professor Koosis' aim is to show how, from simple ideas, one can build up an investigation which explains and clarifies many different, seemingly unrelated problems; to show, in effect, how mathematics grows. The presentation is straightforward, so this, the first of two volumes, is self-contained, but more importantly, by following the theme, Professor Koosis has produced a work that can be read as a whole. He has brought together here many results, some unpublished, some new, and some available only in inaccessible journals.

Preface
Introduction
1. Jensen's formula
2. Szego's theorem
3. Entire functions of exponential type
4. Quasianalyticity
5. The moment problem on the real line
6. Weighted approximation on the real line
7. How small can the Fourier transform of a rapidly decreasing non-zero function be?
8. Persistence of the form dx/(1+x^2)
Addendum
Bibliography for volume I
Index
Contents of volume II.

Subject Areas: Calculus & mathematical analysis [PBK]