Philipp, F."Bessel orbits of normal operators" (2017) Journal of Mathematical Analysis and Applications. 448(2):767-785
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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 constitutes a Bessel sequence. We provide a characterization in terms of the measure ‖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, 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]. © 2016 Elsevier Inc.


Documento: Artículo
Título:Bessel orbits of normal operators
Autor:Philipp, F.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Bessel sequence; Dynamical sampling; Hankel matrix; Hardy space; Toeplitz matrix
Página de inicio:767
Página de fin:785
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.


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---------- APA ----------
(2017) . Bessel orbits of normal operators. Journal of Mathematical Analysis and Applications, 448(2), 767-785.
---------- CHICAGO ----------
Philipp, F. "Bessel orbits of normal operators" . Journal of Mathematical Analysis and Applications 448, no. 2 (2017) : 767-785.
---------- MLA ----------
Philipp, F. "Bessel orbits of normal operators" . Journal of Mathematical Analysis and Applications, vol. 448, no. 2, 2017, pp. 767-785.
---------- VANCOUVER ----------
Philipp, F. Bessel orbits of normal operators. J. Math. Anal. Appl. 2017;448(2):767-785.