The Logarithmic Integral: Volume 1 / Edition 1

by Paul Koosis

Overview

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 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 that 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 He has brought together here many results, some new and unpublished, making this a key reference for graduate students and researchers.

Product Details

ISBN-13:	9780521596725
Publisher:	Cambridge University Press
Publication date:	10/29/1998
Series:	Cambridge Studies in Advanced Mathematics , #12
Edition description:	1 PBK ED
Pages:	628
Product dimensions:	6.10(w) x 9.06(h) x 1.22(d)

Table of Contents

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.

Editorial Reviews

"An inviting, enthusiastic, readable, comprehensive introduction to the logarithmic integral and its many roles..." American Mathematics Monthly

From the Publisher

This is, in the author's hopeful phrase, a "book for reading"--a protracted essay in the form of a graduate-level text, treating (in two volumes) a topic in 20th century analysis which has been a favorite of the author for many years, and which has applications to a rich assortment of subject areas. A secondary objective of the author is methodological, to suggest to young analysts how they might go about the pursuit of their craft, but it is unrealistic to suppose many will (or should) read the book for that primary purpose. Carefully conceived and executed. Of value primarily as a reference work. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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