Navegar

Colección

Datos Estadísticas

Artículo

Heineken, S.; Matusiak, E.; Paternostro, V. "Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications" (2014) International Journal of Wavelets, Multiresolution and Information Processing. 12(2)
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of irregular translates of a bandlimited function in L2(ℝ d). We give conditions for the perturbed sequence to inherit the property of being Riesz or frame sequence. For this case we again calculate the error in the approximation of functions that belong to the perturbed space and compare it with our previous estimation error for general Hilbert spaces. © 2014 World Scientific Publishing Company.

Registro:

Documento: Artículo
Título:Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications
Autor:Heineken, S.; Matusiak, E.; Paternostro, V.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS-CONICET, Buenos Aires, Argentina
Faculty of Mathematics, Universität Wien, NuHAG, Vienna, Austria
Technische Universität Berlin, Institut für Mathematik, Berlin, Germany
Palabras clave:Approximate reconstructions; Bandlimited functions; Canonical duals; Frames; Irregular translates; Riesz bases; Band-limited functions; Canonical duals; Frames; Irregular translates; Riesz basis; Vector spaces; Hilbert spaces
Año:2014
Volumen:12
Número:2
DOI: http://dx.doi.org/10.1142/S0219691314500192
Título revista:International Journal of Wavelets, Multiresolution and Information Processing
Título revista abreviado:Int. J. Wavelets Multiresolution Inf. Process.
ISSN:02196913
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02196913_v12_n2_p_Heineken

Referencias:

  • Aldroubi, A., Gröchenig, K., Nonuniform sampling and reconstruction in shiftinvariant spaces (2001) SIAM Rev, 43 (4), pp. 585-620
  • Balazs, P., Cabrelli, C., Heineken, S., Molter, U., Frames by multiplication current develop (2011) Theory Appl. Wavelets, 5 (2-3), pp. 165-186
  • Balazs, P., Heineken, S., (2013) An Operator Theory Approach to Irregular Frames of Translates Preprint, , arXiv 1401.4955
  • Benedetto, J., Powell, A., Yilmaz, O., Sigma-delta quantization and finite frames (2006) IEEE Trans. Inf. Theory, 52 (5), pp. 1990-2005
  • Beurling, A., Local harmonic analysis with some applications to differential operators (1966) Proc. Ann. Science Conf., Belfer Graduate School of Science, pp. 109-125
  • Bishop, S., Heil, C., Koo, Y.Y., Lim, J.K., Invariances of frame sequences under perturbations (2010) Linear Algebra Appl, 432 (6), pp. 1501-1574
  • Candès, E., Donoho, D., Continuous curvet transform (2005) Appl. Comput. Harmon. Anal, 19, pp. 198-222
  • Casazza, P.G., Christensen, O., Perturbation of operators and applications to frame theory (1997) J. Fourier Anal. Appl, 3, pp. 543-557
  • Casazza, P.G., Christensen, O., Approximation of the inverse frame operator and applications to Gabor frames (2000) J. Approx. Theory, 103 (2), pp. 338-356
  • Christensen, O., A Paley-Wiener theorem for frames (1995) Proc. Amer. Math. Soc, 123, pp. 2199-2202
  • Christensen, O., An introduction to frames and riesz bases (2003) Applied and Numerical Harmonic Analysis (Birkhäuser
  • Christensen, O., Heil, C., (1997) Perturbations of Banach Frames and Atomic Decompositions Math. Nachr, 185, pp. 33-47
  • Christensen, O., Kim, H.O., Kim, R.Y., Lim, J.K., Perturbation of frame sequences in shift-invariant spaces (2005) J. Geom. Anal, 15 (2), pp. 181-192
  • Christensen, O., Laugesen, R.S., Approximately dual frame pairs in Hilbert spaces and applications to Gabor frames (2011) Sampl. Theory Signal Image Process, 9, pp. 77-90
  • Christensen, O., Lennard, C., Lewis, C., (2000) Perturbation of Frames for A Subspace of A Hilbert Space Rocky Mountain J. Math, 30 (4), pp. 1237-1249
  • Daubechies, I., The wavelet transform time-frequency localization and signal analysis (1990) IEEE Trans. Inform. Theory, 36 (5), pp. 961-1005
  • Dörfler, M., Matusiak, E., Nonstationary Gabor frames: Existence and construction, preprint, to appear Int. J. Wavelets Multiresolut. Int. Process
  • Duffin, R., Schaeffer, A., A class of nonharmonic Fourier series (1952) Trans. Amer. Math. Soc, 72, pp. 341-366
  • Eldar, Y.C., Christensen, O., Characterization of oblique dual frame pairs (2006) EURASIP J. Appl. Signal Process, 7. , Article ID 92674
  • Favier, S., Zalik, R., On the stability of frames and riesz bases (1995) Appl. Comput. Harmon. Anal, 2 (2), pp. 160-173
  • Feichtinger, H.G., Molter, U., Romero, J.L., Perturbation techniques in irregular spline-type spaces (2008) Int. J. Wavelets Multiresolut. Inf. Process, 6 (2), pp. 249-277
  • Heil, C., Koo, Y.Y., Lim, J.K., Duals of frame sequences (2009) Acta Appl. Math, 107 (1-3), pp. 75-90
  • Kato, T., (1976) Perturbation Theory for Linear Operators, , Springer
  • Koo, Y.Y., Lim, J.K., Perturbation of frame sequences and its applications to shift-invariant spaces (2007) Linear Algebra Appl, 420 (2-3), pp. 295-309
  • Strohmer, T., Heath, R.W., Grassmannian frames with applications to coding and communication (2003) Appl. Comput. Harmon. Anal, 14 (3), pp. 257-275

Citas:

---------- APA ----------
Heineken, S., Matusiak, E. & Paternostro, V. (2014) . Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications. International Journal of Wavelets, Multiresolution and Information Processing, 12(2).
http://dx.doi.org/10.1142/S0219691314500192
---------- CHICAGO ----------
Heineken, S., Matusiak, E., Paternostro, V. "Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications" . International Journal of Wavelets, Multiresolution and Information Processing 12, no. 2 (2014).
http://dx.doi.org/10.1142/S0219691314500192
---------- MLA ----------
Heineken, S., Matusiak, E., Paternostro, V. "Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications" . International Journal of Wavelets, Multiresolution and Information Processing, vol. 12, no. 2, 2014.
http://dx.doi.org/10.1142/S0219691314500192
---------- VANCOUVER ----------
Heineken, S., Matusiak, E., Paternostro, V. Perturbed frame sequences: Canonical dual systems, approximate reconstructions and applications. Int. J. Wavelets Multiresolution Inf. Process. 2014;12(2).
http://dx.doi.org/10.1142/S0219691314500192