Year: 2011
Type: preprint
Abstract: Let $μ$ be a Borel probability measure with compact support. We consider exponential type orthonormal bases, Riesz bases and frames in $L^2(μ)$. We show that if $L^2(μ)$ admits an exponential frame, then $μ$ must be of pure type. We also classify various $μ$ that admits either kind of exponential bases, in particular, the discrete measures and their connection with integer tiles. By using this and convolution, we construct a class of singularly continuous measures that has an exponential Riesz basis but no exponential orthonormal basis. It is the first of such kind of examples.
Source: arXiv (Cornell University)
Authors: He, Xing-Gang, Lai, Chun-Kit, Lau, Ka-Sing
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: 分形上平方可积函数空间指数型基的研究, 加细分布、样条函数及相关问题的研究
OpenAlex ID: W1585854906