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Extension of Positive-Definite Distributions and Maximum Entropy
Jean-Pierre Gabardo

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$36
Individual Members: US$21.60
Institutional Members: US$28.80
Order Code: MEMO/102/489
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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.

Table of Contents

  • 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
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