Stable Truncated Trigonometric Moment Problems

Authors

DOI:

https://doi.org/10.37256/cm.5420245096

Keywords:

full and truncated trigonometric moment problems, liniar unital functional positive on squares, unitary operators, dimensional stability, representing measure

Abstract

Let mceclip7.png, mceclip6.png be an one dimensional complex sequence of degree at most 2n. In the present paper we give a necessary condition such that mceclip1-2d1c9ac22af0a35cd9cbda2cfb3f8d60.png admits on mceclip1.png an atomic representing measure with a finite number of atoms. The necessary condition is expressed in terms of "stability" of the Riesz linear non-negative functional, blobid0.png, associated to the given sequence. We also give a necessary and sufficient condition such that the extended sequence mceclip5.png to admit on blobid1.png an unique atomic representing measure with a finite number of atoms. The "stability" condition of the introduced Riesz functional is an adaption of the concept "dimension stability" by Vasilescu introduced for solving Hamburger moment problems in [5]. In section 3 of the present paper, we apply the main existence theorem for determining representing measures with 1, 2, 3 atoms, according to the rank of the moment matrix. The representing measures of the data of the quadratic moment problem have the support in the unit circle.

Downloads

Published

2024-11-22

How to Cite

1.
Ninulescu LL. Stable Truncated Trigonometric Moment Problems. Contemp. Math. [Internet]. 2024 Nov. 22 [cited 2024 Dec. 4];5(4):5382-94. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/5096