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Extension of Positive-Definite Distributions and Maximum Entropy

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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 Click above image for expanded view Extension of Positive-Definite Distributions and Maximum Entropy Available Formats:  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
• Book Details

Memoirs of the American Mathematical Society
Volume: 1021993; 94 pp
MSC: 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.

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
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Volume: 1021993; 94 pp
MSC: 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.

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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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