A generalized trigonometric moment problem in a weighted L2(−∞,0) space

Elias Zikkos

doi:10.1016/j.jmaa.2021.125675

A generalized trigonometric moment problem in a weighted L²(−∞,0) space

Elias Zikkos

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Abstract

In this paper we consider a generalized trigonometric moment problem in a weighted L²(−∞,0) space. We obtain a solution which is in the closed span of some exponential system E_Λ={t^ke^iλ_nt} in the weighted space. Our motivation is a classical trigonometric moment problem in L²(−π,π). Based on an entire function, a lower bound for the distance between exponential functions and the closed span of the remaining elements of the system E_Λ is derived. An upper bound is then obtained for the norm of the elements of a biorthogonal system to E_Λ. The proof of our result utilizes the notions of Bessel sequences and Riesz-Fischer sequences.

Original language	British English
Article number	125675
Journal	Journal of Mathematical Analysis and Applications
Volume	506
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2021.125675
State	Published - 15 Feb 2022

Keywords

Bessel sequences
Biorthogonal families
Exponential systems
Moment problems
Riesz-Fischer sequences

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10.1016/j.jmaa.2021.125675

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abstract = "In this paper we consider a generalized trigonometric moment problem in a weighted L2(−∞,0) space. We obtain a solution which is in the closed span of some exponential system EΛ={tkeiλnt} in the weighted space. Our motivation is a classical trigonometric moment problem in L2(−π,π). Based on an entire function, a lower bound for the distance between exponential functions and the closed span of the remaining elements of the system EΛ is derived. An upper bound is then obtained for the norm of the elements of a biorthogonal system to EΛ. The proof of our result utilizes the notions of Bessel sequences and Riesz-Fischer sequences.",

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AU - Zikkos, Elias

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N2 - In this paper we consider a generalized trigonometric moment problem in a weighted L2(−∞,0) space. We obtain a solution which is in the closed span of some exponential system EΛ={tkeiλnt} in the weighted space. Our motivation is a classical trigonometric moment problem in L2(−π,π). Based on an entire function, a lower bound for the distance between exponential functions and the closed span of the remaining elements of the system EΛ is derived. An upper bound is then obtained for the norm of the elements of a biorthogonal system to EΛ. The proof of our result utilizes the notions of Bessel sequences and Riesz-Fischer sequences.

AB - In this paper we consider a generalized trigonometric moment problem in a weighted L2(−∞,0) space. We obtain a solution which is in the closed span of some exponential system EΛ={tkeiλnt} in the weighted space. Our motivation is a classical trigonometric moment problem in L2(−π,π). Based on an entire function, a lower bound for the distance between exponential functions and the closed span of the remaining elements of the system EΛ is derived. An upper bound is then obtained for the norm of the elements of a biorthogonal system to EΛ. The proof of our result utilizes the notions of Bessel sequences and Riesz-Fischer sequences.

KW - Bessel sequences

KW - Biorthogonal families

KW - Exponential systems

KW - Moment problems

KW - Riesz-Fischer sequences

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DO - 10.1016/j.jmaa.2021.125675

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AN - SCOPUS:85115916263

SN - 0022-247X

VL - 506

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 125675

ER -

A generalized trigonometric moment problem in a weighted L²(−∞,0) space

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