Hausdorff Moment Sequences Induced by Rational Functions
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

Author

Md Ramiz Reza

Indian Institute of Technology, Kanpur

Genkai Zhang

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Complex Analysis and Operator Theory

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

Vol. 13 8 4117-4142

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1007/s11785-019-00952-9

More information

Latest update

11/8/2019