Memoirs of the American Mathematical Society 1993; 94 pp; softcover Volume: 102 ISBN10: 0821825518 ISBN13: 9780821825518 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 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. Readership Research Mathematicians. Table of Contents  Facts and definitions
 The discrete case
 Positivedefinite distributions on an interval \((A,A)\)
 The nondegenerate case
 A closure problem in \(L^2_\mu (\hat {\mathbb R})\)
 Entropy maximizing measures in \(\scr M_A(Q)\)
 Uniqueness of the extension
