| Electronic ISBN: | 978-1-4704-0066-8 |
| Product Code: | MEMO/102/489.E |
| List Price: | $36.00 |
| MAA Member Price: | $32.40 |
| AMS Member Price: | $21.60 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 102; 1993; 94 ppMSC: Primary 42; Secondary 46;
In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.
ReadershipResearch Mathematicians.
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Table of Contents
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Chapters
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1. The discrete case
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2. Positive-definite distributions on an interval $(-A, A)$
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3. The non-degenerate case
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4. A closure problem in $L^2_\mu (\hat {\mathbb {R}})$
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5. Entropy maximizing measures in $\mathcal {M}_A(Q)$
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6. Uniqueness of the extension
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In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.
Research Mathematicians.
-
Chapters
-
1. The discrete case
-
2. Positive-definite distributions on an interval $(-A, A)$
-
3. The non-degenerate case
-
4. A closure problem in $L^2_\mu (\hat {\mathbb {R}})$
-
5. Entropy maximizing measures in $\mathcal {M}_A(Q)$
-
6. Uniqueness of the extension
