Bessel orbits of normal operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

Philipp, Friedrich¹ 

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, Ciudad Univ,Pabellon 1, RA-1428 Buenos Aires, DF, Argentina

关键词: Bessel sequence;    Dynamical sampling;    Hardy space;    Hankel matrix;    Toeplitz matrix;   

DOI  :  10.1016/j.jmaa.2016.11.009

来源: Elsevier

【 摘 要 】

Given a bounded normal operator A in a Hilbert space and a fixed vector x, we elaborate on the problem of finding necessary and sufficient conditions under which (A(k)x)(k is an element of N) constitutes a Bessel sequence. We provide a characterization in terms of the measure vertical bar vertical bar E(.)x vertical bar vertical bar(2), where E is the spectral measure of the operator A. In the separately treated special cases where A is unitary or selfadjoint we obtain more explicit characterizations. Finally, we apply our results to a sequence (A(k)x)(k is an element of N), where A arises from the heat equation. The problem is motivated by and related to the new field of Dynamical Sampling which was recently initiated by Aldroubi et al. in [3]. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free