Bessel orbits of normal operators

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• 作者：Friedrich Philipp ^{fmphilipp@gmail.com}
• 关键词：Bessel sequence ; Dynamical sampling ; Hardy space ; Hankel matrix ; Toeplitz matrix
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：767-785
• 全文大小：470 K
• 卷排序：448

文摘

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)k∈N(Akx)k∈N constitutes a Bessel sequence. We provide a characterization in terms of the measure ‖E(⋅)x‖^{2‖E(⋅)x‖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 (Akx)k∈N(Akx)k∈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].}