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Other titles in the Cambridge Studies in Advanced Mathematics series:
Cambridge Studies in Advanced Mathematics #012: The Logarithmic Integral: Volume 1by Paul Koosis
Synopses & Reviews
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 He has brought together here many results, some new and unpublished, making this a key reference for graduate students and researchers.
The logarithmic integral is a thread connecting many apparently separate parts of twentieth century analysis, 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.
Self-contained study of real and complex analysis bringing together many separate parts of this subject.
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.
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