A problem on completeness of exponentials
成果类型：
Article
署名作者：
Poltoratski, A.
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2013.178.3.4
发表日期：
2013
页码：
983-1016
关键词：
摘要：
Let mu be a finite positive measure on the real line. For a > 0, denote by epsilon(a) the family of exponential functions epsilon(a) - {epsilon(ist) vertical bar s is an element of[0, a]}. The exponential type of mu is the infimum of all numbers a such that the finite linear combinations of the exponentials from epsilon(a) are dense in L-2 (mu). If the set of such a is empty, the exponential type of mu is defined as infinity. The well-known type problem asks to find the exponential type of mu in terms of mu. In this note we present a solution to the type problem and discuss its relations with known results.