Electronic ISBN:  9781470400668 
Product Code:  MEMO/102/489.E 
List Price:  $36.00 
MAA Member Price:  $32.40 
AMS Member Price:  $21.60 

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 positivedefinite 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.

Table of Contents

Chapters

1. The discrete case

2. Positivedefinite distributions on an interval $(A, A)$

3. The nondegenerate 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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In this work, the maximum entropy method is used to solve the extension problem associated with a positivedefinite 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. Positivedefinite distributions on an interval $(A, A)$

3. The nondegenerate 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