Aldroubi, A.; Cabrelli, C.; Molter, U.; Tang, S. "Dynamical sampling" (2017) Applied and Computational Harmonic Analysis. 42(3):378-401
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Let Y={f(i),Af(i),…,Alif(i):i∈Ω}, where A is a bounded operator on ℓ2(I). The problem under consideration is to find necessary and sufficient conditions on A,Ω,{li:i∈Ω} in order to recover any f∈ℓ2(I) from the measurements Y. This is the so-called dynamical sampling problem in which we seek to recover a function f by combining coarse samples of f and its futures states Alf. We completely solve this problem in finite dimensional spaces, and for a large class of self adjoint operators in infinite dimensional spaces. In the latter case, although Y can be complete, using the Müntz–Szász Theorem we show it can never be a basis. We can also show that, when Ω is finite, Y is not a frame except for some very special cases. The existence of these special cases is derived from Carleson's Theorem for interpolating sequences in the Hardy space H2(D). Finally, using the recently proved Kadison–Singer/Feichtinger theorem we show that the set obtained by normalizing the vectors of Y can never be a frame when Ω is finite. © 2015 Elsevier Inc.


Documento: Artículo
Título:Dynamical sampling
Autor:Aldroubi, A.; Cabrelli, C.; Molter, U.; Tang, S.
Filiación:Department of Mathematics, Vanderbilt University, Nashville, TN 37240-0001, United States
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Palabras clave:Carleson's theorem; Feichtinger conjecture; Frames; Müntz–Szász Theorem; Reconstruction; Sampling theory; Sub-sampling; Harmonic analysis; Image reconstruction; Carleson's theorem; Feichtinger conjecture; Frames; Sampling theory; Sub-sampling; Problem solving
Página de inicio:378
Página de fin:401
Título revista:Applied and Computational Harmonic Analysis
Título revista abreviado:Appl Comput Harmonic Anal


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---------- APA ----------
Aldroubi, A., Cabrelli, C., Molter, U. & Tang, S. (2017) . Dynamical sampling. Applied and Computational Harmonic Analysis, 42(3), 378-401.
---------- CHICAGO ----------
Aldroubi, A., Cabrelli, C., Molter, U., Tang, S. "Dynamical sampling" . Applied and Computational Harmonic Analysis 42, no. 3 (2017) : 378-401.
---------- MLA ----------
Aldroubi, A., Cabrelli, C., Molter, U., Tang, S. "Dynamical sampling" . Applied and Computational Harmonic Analysis, vol. 42, no. 3, 2017, pp. 378-401.
---------- VANCOUVER ----------
Aldroubi, A., Cabrelli, C., Molter, U., Tang, S. Dynamical sampling. Appl Comput Harmonic Anal. 2017;42(3):378-401.