Artículo

Aldroubi, A.; Cabrelli, C.; Çakmak, A.F.; Molter, U.; Petrosyan, A. "Iterative actions of normal operators" (2017) Journal of Functional Analysis. 272(3):1121
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Abstract:

Let A be a normal operator in a Hilbert space H, and let G⊂H be a countable set of vectors. We investigate the relations between A, G and L that make the system of iterations {Ang:g∈G,0≤n<L(g)} complete, Bessel, a basis, or a frame for H. The problem is motivated by the dynamical sampling problem and is connected to several topics in functional analysis, including, frame theory and spectral theory. It also has relations to topics in applied harmonic analysis including, wavelet theory and time-frequency analysis. © 2016 Elsevier Inc.

Registro:

Documento: Artículo
Título:Iterative actions of normal operators
Autor:Aldroubi, A.; Cabrelli, C.; Çakmak, A.F.; Molter, U.; Petrosyan, A.
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
IMAS, UBA-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Department of Mathematical Engineering, Yildiz Technical Univ., Davutpaşa Campus, Esenler, İstanbul, 80750, Turkey
Palabras clave:Dynamics; Frames; Sampling
Año:2017
Volumen:272
Número:3
Página de inicio:1121
DOI: http://dx.doi.org/10.1016/j.jfa.2016.10.027
Título revista:Journal of Functional Analysis
Título revista abreviado:J. Funct. Anal.
ISSN:00221236
CODEN:JFUAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v272_n3_p1121_Aldroubi

Referencias:

  • Abrahamse, M.B., Kriete, T.L., The spectral multiplicity of a multiplication operator (1973) Indiana Univ. Math. J., 22, pp. 845-857
  • Aldroubi, A., Baskakov, A.G., Krishtal, I.A., Slanted matrices, Banach frames, and sampling (2008) J. Funct. Anal., 255 (7), pp. 1667-1691
  • Aldroubi, A., Cabrelli, C., Molter, U., Tang, S., Dynamical sampling (2016) Appl. Comput. Harmon. Anal., , in press, arXiv:1409.8333
  • Aldroubi, A., Davis, J., Krishtal, I., Exact reconstruction of signals in evolutionary systems via spatiotemporal trade-off (2015) J. Fourier Anal. Appl., 21, pp. 11-31
  • Barbieri, D., Hernández, E., Parcet, J., Riesz and frame systems generated by unitary actions of discrete groups (2015) Appl. Comput. Harmon. Anal., 39 (3), pp. 369-399
  • Barbieri, D., Hernández, E., Paternostro, V., The Zak transform and the structure of spaces invariant by the action of an LCA group (2015) J. Funct. Anal., 269 (5), pp. 1327-1358
  • Bownik, M., Speegle, D., The Feichtinger conjecture for wavelet frames, Gabor frames and frames of translates (2006) Canad. J. Math., 58 (6), pp. 1121-1143
  • Casazza, P.G., Tremain, J.C., The Kadison–Singer problem in mathematics and engineering (2006) Proc. Natl. Acad. Sci. USA, 103 (7), pp. 2032-2039. , (electronic)
  • Christensen, J.G., Mayeli, A., Ólafsson, G., Coorbit description and atomic decomposition of Besov spaces (2012) Numer. Funct. Anal. Optim., 33 (7-9), pp. 847-871
  • Christensen, O., Frames and Bases. An Introductory Course (2008) Appl. Numer. Harmon. Anal., , Birkhäuser Boston Inc. Boston, MA
  • Conway, J.B., Subnormal Operators (1981) Res. Notes Math., 51. , Pitman (Advanced Publishing Program) Boston, MA, London
  • Conway, J.B., A Course in Functional Analysis (1994) Grad. Texts in Math., , 2 edition Springer
  • Davis, J., Dynamical sampling with a forcing term (2014) Operator Methods in Wavelets, Tilings, and Frames, Contemp. Math., 626, pp. 167-177. , Veronika Furst Keri A. Kornelson Eric S. Weber Amer. Math. Soc. Providence, RI
  • Duffin, R.J., Schaeffer, A.C., A class of nonharmonic Fourier series (1952) Trans. Amer. Math. Soc., 72, pp. 341-366
  • Dutkay, D.E., Jorgensen, P.E.T., Spectra of measures and wandering vectors (2015) Proc. Amer. Math. Soc., 143 (6), pp. 2403-2410
  • Dutkay, D.E.E., Jorgensen, P.E.T., Unitary groups and spectral sets (2015) J. Funct. Anal., 268 (8), pp. 2102-2141
  • Dyer, J.A., Pedersen, E.A., Porcelli, P., An equivalent formulation of the invariant subspace conjecture (1972) Bull. Amer. Math. Soc., (78), pp. 1020-1023
  • Gröchenig, K., Ortega-Cerdà, J., Romero, J.L., Deformation of Gabor systems (2015) Adv. Math., 277, pp. 388-425
  • Gröchenig, K., Romero, J.L., Unnikrishnan, J., Vetterli, M., On minimal trajectories for mobile sampling of bandlimited fields (2015) Appl. Comput. Harmon. Anal., 39 (3), pp. 487-510
  • Halmos, P.R., Normal dilations and extensions of operators (1950) Summa Brasil. Math., 2, pp. 125-134
  • Han, D., The existence of tight Gabor duals for Gabor frames and subspace Gabor frames (2009) J. Funct. Anal., 256 (1), pp. 129-148
  • Han, D., Larson, D.R., Frames, bases and group representations (2000) Mem. Amer. Math. Soc., 147 (697). , x+94
  • Hayman, W., Interpolation by bounded functions (1958) Ann. Inst. Fourier (Grenoble), 8, pp. 277-290
  • Heil, C., A Basis Theory Primer (2011) Appl. Numer. Harmon. Anal., , Birkhäuser/Springer New York expanded edition
  • Hormati, A., Roy, O., Lu, Y.M., Vetterli, M., Distributed sampling of signals linked by sparse filtering: theory and applications (2010) IEEE Trans. Signal Process., 58 (3), pp. 1095-1109. , March
  • Kaznelson, Y., An Introduction to Harmonic Analysis (2004), 3 edition Cambridge University Press; Kriete, T.L., III, An elementary approach to the multiplicity theory of multiplication operators (1986) Rocky Mountain J. Math., 16 (1), pp. 23-32
  • Kubrusly, C.S., Spectral Theory of Operators on Hilbert Spaces (2012), Birkhäuser/Springer New York; Larson, D., Scholze, S., Signal reconstruction from frame and sampling erasures (2015) J. Fourier Anal. Appl., 21 (5), pp. 1146-1167
  • Marcus, A.W., Spielman, D.A., Srivastava, N., Interlacing families II: mixed characteristic polynomials and the Kadison–Singer problem (2015) Ann. of Math., 182 (1), pp. 327-350
  • Nashed, M.Z., Sun, Q., Sampling and reconstruction of signals in a reproducing kernel subspace of Lp(Rd) (2010) J. Funct. Anal., 258 (7), pp. 2422-2452
  • Nikol'skiĭ, N.K., Treatise on the shift operator (1986) Spectral Function Theory, Grundlehren Math. Wiss., 273. , S.V. Hruščev S.V. Khrushchëv V.V. Peller Fundamental Principles of Mathematical Sciences Springer-Verlag Berlin With an appendix by S.V. Hruščev [S.V. Khrushchëv] and V.V. Peller. Translated from Russian by Jaak Peetre
  • Nikol'skiĭ, N.K., Multicyclicity phenomenon. I. An introduction and maxi-formulas (1989) Toeplitz Operators and Spectral Function Theory, Oper. Theory Adv. Appl., 42, pp. 9-57. , Birkhäuser Basel
  • Nikol'skiĭ, N.K., Vasjunin, V.I., Control subspaces of minimal dimension, unitary and model operators (1983) J. Operator Theory, 10 (2), pp. 307-330
  • Rudin, W., Real and Complex Analysis (1986) Internat. Ser. Pure Appl. Math., , 3 edition McGraw–Hill Science/Engineering/Math
  • Scroggs, J.E., Invariant subspaces of a normal operator (1959) Duke Math. J., 26, pp. 95-111
  • Sun, Q., Local reconstruction for sampling in shift-invariant spaces (2010) Adv. Comput. Math., 32 (3), pp. 335-352
  • Sun, Q., Localized nonlinear functional equations and two sampling problems in signal processing (2014) Adv. Comput. Math., 40 (2), pp. 415-458
  • Treil, S., Unconditional bases of invariant subspaces of a contraction with finite defects (1997) Indiana Univ. Math. J., 46 (4), pp. 1021-1054
  • Weber, E., Wavelet transforms and admissible group representations (2008) Representations, Wavelets, and Frames, Appl. Numer. Harmon. Anal., pp. 47-67. , Birkhäuser Boston Boston, MA
  • Wermer, J., On invariant subspaces of normal operators (1952) Proc. Amer. Math. Soc., 3, pp. 270-277

Citas:

---------- APA ----------
Aldroubi, A., Cabrelli, C., Çakmak, A.F., Molter, U. & Petrosyan, A. (2017) . Iterative actions of normal operators. Journal of Functional Analysis, 272(3), 1121.
http://dx.doi.org/10.1016/j.jfa.2016.10.027
---------- CHICAGO ----------
Aldroubi, A., Cabrelli, C., Çakmak, A.F., Molter, U., Petrosyan, A. "Iterative actions of normal operators" . Journal of Functional Analysis 272, no. 3 (2017) : 1121.
http://dx.doi.org/10.1016/j.jfa.2016.10.027
---------- MLA ----------
Aldroubi, A., Cabrelli, C., Çakmak, A.F., Molter, U., Petrosyan, A. "Iterative actions of normal operators" . Journal of Functional Analysis, vol. 272, no. 3, 2017, pp. 1121.
http://dx.doi.org/10.1016/j.jfa.2016.10.027
---------- VANCOUVER ----------
Aldroubi, A., Cabrelli, C., Çakmak, A.F., Molter, U., Petrosyan, A. Iterative actions of normal operators. J. Funct. Anal. 2017;272(3):1121.
http://dx.doi.org/10.1016/j.jfa.2016.10.027