On indeterminate Hamburger moment problems

Hamburger Moment Problems and Orthogonal Polynomials

We consider a sequence of orthogonal polynomials given by the classical three term recurrence relation. We address the problem of deciding the determinacy or indeterminacy of the associated Hamburger moment problem on the basis of the behavior of the coefficients in the three term recurrence relation. Comparisons are made with other criteria in the literature. The efficacy of the criteria obtai...

On the order of indeterminate moment problems

For an indeterminate moment problem we denote the orthonormal polynomials by Pn. We study the relation between the growth of the function P (z) = ( ∑∞ n=0 |Pn(z)|) and summability properties of the sequence (Pn(z)). Under certain assumptions on the recurrence coefficients from the three term recurrence relation zPn(z) = bnPn+1(z) + anPn(z) + bn−1Pn−1(z), we show that the function P is of order ...

On in nitely divisible solutions to indeterminate moment problems

Entropy-convergence, Instability in Stieltjes and Hamburger Moment Problems

The recovering of a positive density, of which a nite number of moments is assigned, is considered (in the Stieltjes and Hamburger moment problems). In the choice of the approximant the Maximum Entropy approach is adopted. Two main problems are taken into account. 1. A review of diierent criteria concerning the determinacy and indeterminacy of the innnite moment problem is presented. This revie...

Holomorphic functions associated with indeterminate rational moment problems

We consider indeterminate rational moment problems on the real line with their associated orthogonal rational functions. There exists a Nevanlinna type parameterization relating to the problem, with associated Nevanlinna matrices of functions having singularities in the closure of the set of poles of the rational functions belonging to the problem. We prove that the growth at the isolated singu...