Journal article, 2019

We study the Hausdorff moment problem for a class of sequences, namely (r(n))n∈Z+, where r is a rational function in the complex plane. We obtain a necessary condition for such sequence to be a Hausdorff moment sequence. We found an interesting connection between Hausdorff moment problem for this class of sequences with finite divided differences and convolution of complex exponential functions. We provide a sufficient condition on the zeros and poles of a rational function r so that (r(n))n∈Z+ is a Hausdorff moment sequence. G. Misra asked whether the module tensor product of a subnormal module with the Hardy module over the polynomial ring is again a subnormal module or not. Using our necessary condition we answer the question of G. Misra in negative. Finally, we obtain a characterization of all real polynomials p of degree up to 4 and a certain class of real polynomials of degree 5 for which the sequence (1/p(n))n∈Z+ is a Hausdorff moment sequence.

Positive definite kernel

Module tensor product

Subnormality

Moment problem

Indian Institute of Technology, Kanpur

Chalmers, Mathematical Sciences, Analysis and Probability Theory

1661-8254 (ISSN) 1661-8262 (eISSN)

Vol. 13 8 4117-4142Algebra and Logic

Geometry

Mathematical Analysis

10.1007/s11785-019-00952-9