Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775260 | Journal of Mathematical Analysis and Applications | 2017 | 19 Pages |
Abstract
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 (Akx)kâN constitutes a Bessel sequence. We provide a characterization in terms of the measure âE(â
)xâ2, 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 (Akx)kâN, 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].
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Friedrich Philipp,