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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)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.

Registro:

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, Argentina
Palabras clave:Bessel sequence; Dynamical sampling; Hankel matrix; Hardy space; Toeplitz matrix
Año:2017
Volumen:448
Número:2
Página de inicio:767
Página de fin:785
DOI: http://dx.doi.org/10.1016/j.jmaa.2016.11.009
ISSN:0022247X
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_0022247X_v448_n2_p767_Philipp

Referencias:

  • Aldroubi, A., Aceska, R., Davis, J., Petrosyan, A., Dynamical sampling in shift-invariant spaces (2013) Contemp. Math., 603, pp. 139-148. , AMS
  • Aldroubi, A., Cabrelli, C., Çakmak, A.F., Molter, U., Petrosyan, A., Iterative actions of normal operators (2016) J. Funct. Anal., , in press
  • Aldroubi, A., Cabrelli, C., Molter, U., Tang, S., Dynamical sampling (2016) Appl. Comput. Harmon. Anal., , in press
  • Aldroubi, A., Davis, J., Krishtal, I., Dynamical sampling: time space trade-off (2013) Appl. Comput. Harmon. Anal., 34, pp. 495-503
  • Aldroubi, A., Petrosyan, A., Dynamical sampling and systems from iterative actions of operators, preprint; Beauzamy, B., Introduction to Operator Theory and Invariant Subspaces (1988), Elsevier Science Publishers; Böttcher, A., Grudsky, S.M., Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis (2000), Springer Basel AG; Carleson, L., On convergence and growth of partial sums of Fourier series (1966) Acta Math., 116, pp. 135-157
  • Christensen, O., An Introduction to Frames and Riesz Bases (2003), Birkhäuser Boston, Basel, Berlin; Douglas, R.G., Banach Algebra Techniques in Operator Theory (1972), Acad. Press; Garnett, J.B., Bounded Analytic Functions (2007), revised first edition Springer Science+Business Media, LLC New York; Hardy, G.H., Littlewood, J.E., Pólya, G., Inequalities (1934), Cambridge University Press; Hormati, A., Roy, O., Lu, Y., Vetterli, M., Distributed sampling of signals linked by sparse filtering: theory and applications (2010) IEEE Trans. Signal Process., 58, pp. 1095-1109
  • Kaznelson, Y., An Introduction to Harmonic Analysis (2004), Cambridge University Press; Lu, Y., Vetterli, M., Spatial super-resolution of a diffusion field by temporal oversampling in sensor networks (2009) IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2009, April 2009, pp. 2249-2252
  • Nehari, Z., On bounded bilinear forms (1957) Ann. of Math., 65, pp. 153-162
  • Nikolskii, N., Operators, Functions and Systems: An Easy Reading, Vol. I: Hardy, Hankel, and Toeplitz (2002) Math. Surveys Monogr., 92. , AMS Providence
  • Ranieri, J., Chebira, A., Lu, Y.M., Vetterli, M., Sampling and reconstructing diffusion fields with localized sources (2011) IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, May 2011, pp. 4016-4019
  • Rudin, W., Real and Complex Analysis (1987), third edition McGraw–Hill Book Company; Wermer, J., On invariant subspaces of normal operators (1952) Proc. Amer. Math. Soc., 3, pp. 270-277
  • Widom, H., Hankel matrices (1966) Trans. Amer. Math. Soc., 121, pp. 1-35
  • Woracek, H., Komplexe Analysis im Einheitskreis, Lecture notes, 2004; Yafaev, D.R., Unbounded Hankel operators and moment problems (2016) Integral Equ. Oper. Theory, 85, pp. 289-300

Citas:

---------- APA ----------
(2017) . Bessel orbits of normal operators, 448(2), 767-785.
http://dx.doi.org/10.1016/j.jmaa.2016.11.009
---------- CHICAGO ----------
Philipp, F. "Bessel orbits of normal operators" 448, no. 2 (2017) : 767-785.
http://dx.doi.org/10.1016/j.jmaa.2016.11.009
---------- MLA ----------
Philipp, F. "Bessel orbits of normal operators" , vol. 448, no. 2, 2017, pp. 767-785.
http://dx.doi.org/10.1016/j.jmaa.2016.11.009
---------- VANCOUVER ----------
Philipp, F. Bessel orbits of normal operators. 2017;448(2):767-785.
http://dx.doi.org/10.1016/j.jmaa.2016.11.009