A Family of Heat Functions as Solutions of Indeterminate Moment Problems

From Discrete to Absolutely Continuous Solutions of Indeterminate Moment Problems

We consider well-known families of discrete solutions to indeterminate moment problems and show how they can be used in a simple way to generate absolutely continuous solutions to the same moment problems. The following cases are considered: log-normal, generalized Stieltjes-Wigert, q-Laguerre and discrete q-Hermite II.

On in nitely divisible solutions to indeterminate moment problems

On some indeterminate moment problems for measures on a geometric progression

We consider some indeterminate moment problems which all have a discrete solution concentrated on geometric progressions of the form cq ; k ∈Z or ± cq ; k ∈Z. It turns out to be possible that such a moment problem has in nitely many solutions concentrated on the geometric progression. c © 1998 Elsevier Science B.V. All rights reserved. AMS classi cation: primary 44A60; secondary 33A65; 33D45

Logarithmic order and type of indeterminate moment problems II

This paper deals with the indeterminate moment problem on the real line. We are given a positive measure μ on R having moments of all orders and we assume that μ is not determined by its moments. For details about the indeterminate moment problem see the monographs by Akhiezer, by Shohat and Tamarkin or the survey paper by Berg. Our notation follows that of Akhiezer. In this indeterminate situa...

Natural solutions of rational Stieltjes moment problems

In the strong or two-point Stieltjes moment problem, one has to find a positive measure on [0,∞) for which infinitely many moments are prescribed at the origin and at infinity. Here we consider a multipoint version in which the origin and the point at infinity are replaced by sequences of points that may or may not coincide. In the indeterminate case, two natural solutions μ0 and μ∞ exist that ...