From Discrete to Absolutely Continuous Solutions of Indeterminate Moment Problems

Self-adjoint difference operators and classical solutions to the Stieltjes-Wigert moment problem

Abstract. The Stieltjes–Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted L-spaces. Under some additional assumptions these measures are exactly the solutions to the q-Pear...

The Killip–simon Theorem: Szegő for Oprl

By structure of the set of solutions, we mean is it closed in the weak topology? (This is not obvious since x is not bounded.) Is it of finite or infinite dimension? Among the solutions, are there any that are pure point or singular continuous or purely absolutely continuous? If there exists a unique solution, we call the moment problem determinate, and if there are multiple solutions, indeterm...

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

A novel technique for a class of singular boundary value problems

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

On in nitely divisible solutions to indeterminate moment problems