Extension of Positive-Definite Distributions and Maximum Entropy

· American Mathematical Society: Memoirs of the American Mathematical Society Book 489 · American Mathematical Soc.
Ebook
94
Pages
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About this ebook

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.

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