2019/03/01 by Md. Ramiz Reza, Reza, Md. Ramiz, Genkai Zhang +1
Mathematics · #44A60 #46E22 #47B20 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1903.00116
openalex publication_date 2019/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Hausdorff moment problem for a class of sequences, namely (r(n))n∈\mathbb 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∈\mathbb 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∈\mathbb Z+ is a Hausdorff moment sequence.