Completeness of certain exponential systems and zeros of lacunary polynomials

被引：0
|
作者：
Kulikov, Aleksei [1 ,2 ]
Ulanovskii, Alexander [3 ]
Zlotnikov, Ilya [3 ,4 ]
机构：
[1] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway
[2] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel
[3] Univ Stavanger, Dept Math & Phys, N-4036 Stavanger, Norway
[4] Univ Vienna, Fac Math, NuHAG, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
来源：
ADVANCES IN MATHEMATICS | 2023年 / 421卷
基金：
奥地利科学基金会;
关键词：
Completeness; Frame; Totally positive matrix; Generalized Vandermonde matrix; Uniqueness set; Lacunary polynomials;
D O I：
10.1016/j.aim.2023.109016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let I' be a subset of {0, 1, 2, ...}. We show that if I' has 'gaps' then the completeness and frame properties of the system {tke2 pi int : n is an element of Z, k is an element of I'} differ from those of the classical exponential systems. This phenomenon is closely connected with the existence of certain uniqueness sets for lacunary polynomials.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
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页数：17
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