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Extension of Positive-Definite Distributions and Maximum Entropy
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Memoirs of the American Mathematical Society
1993; 94 pp; softcover
Volume: 102
ISBN-10: 0-8218-2551-8
ISBN-13: 978-0-8218-2551-8
List Price: US$34 Individual Members: US$20.40
Institutional Members: US\$27.20
Order Code: MEMO/102/489

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.

• Facts and definitions
• The discrete case
• Positive-definite distributions on an interval $$(-A,A)$$
• The non-degenerate case
• A closure problem in $$L^2_\mu (\hat {\mathbb R})$$
• Entropy maximizing measures in $$\scr M_A(Q)$$
• Uniqueness of the extension