Indeterminate symmetric moment problems

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 ...

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...

From asymptotics to spectral measures: determinate versus indeterminate moment problems

In the field of orthogonal polynomials theory, the classical Markov theorem shows that for determinate moment problems the spectral measure is under control of the polynomials asymptotics. The situation is completely different for indeterminate moment problems, in which case the interesting spectral measures are to be constructed using Nevanlinna theory. Nevertheless it is interesting to observ...

On in nitely divisible solutions to 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.