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Cabrelli, C.; Molter, U.; Lee, D.G.; Pfander, G.E.; Anbarjafari G.; Kivinukk A.; Tamberg G. "Extra invariance and Balian-Low type obstructions for Gabor spaces" (2017) 12th International Conference on Sampling Theory and Applications, SampTA 2017:391-395
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Abstract:

We establish some Balian-Low type results for Gabor spaces, which concern with discontinuity in some periodization of Z φ , where Z φ is the Zak transform of the window function φ ϵ L 2 (ℝ d ). The results are compared with the case for shift-invariant spaces where the Zak transform is replaced by Fourier transform. © 2017 IEEE.

Registro:

Documento: Conferencia
Título:Extra invariance and Balian-Low type obstructions for Gabor spaces
Autor:Cabrelli, C.; Molter, U.; Lee, D.G.; Pfander, G.E.; Anbarjafari G.; Kivinukk A.; Tamberg G.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
IMAS/CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Lehrstuhl für Mathematik - Wissenschaftliches Rechnen, Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt-Ingolstadt, Eichstätt, 85071, Germany
Palabras clave:Shift-invariant space; Window functions
Año:2017
Página de inicio:391
Página de fin:395
DOI: http://dx.doi.org/10.1109/SAMPTA.2017.8024416
Título revista:12th International Conference on Sampling Theory and Applications, SampTA 2017
Título revista abreviado:Int. Conf. Sampl. Theory Appl., SampTA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97815386_v_n_p391_Cabrelli

Referencias:

  • Aldroubi, A., Cabrelli, C., Heil, C., Kornelson, K., Molter, U., Invariance of a shift-invariant space (2010) J. Fourier Anal. Appl., 16 (1), pp. 60-75
  • Anastasio, M., Cabrelli, C., Paternostro, V., Invariance of a shift-invariant space in several variables (2011) Complex Anal. Oper. Theory, 5 (4), pp. 1031-1050
  • Aldroubi, A., Sun, Q., Wang, H., Uncertainty principles and Balian-Low type theorems in principal shift-invariant spaces (2011) Appl. Comput. Harmon. Anal., 30 (3), pp. 337-347
  • Balian, R., Un principe d'incertitude fort en théorie du signal ou en mécanique quantique (1981) C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre, 292 (20), pp. 1357-1362
  • Benedetto, J.J., Heil, C., Walnut, D.F., Differentiation and the Balian-Low theorem (1995) J. Fourier Anal. Appl., 1 (4), pp. 355-402
  • Christensen, O., (2003) An Introduction to Frames and Riesz Bases, , Birkhäuser, Boston
  • Cabrelli, C., Lee, D.G., Molter, U., Pfander, G.E., (2017) Timefrequency Shift Invariance of Gabor Spaces Generated by Integer Lattices, , preprint, arXiv:1705. 02495
  • Cabrelli, C., Molter, U., Pfander, G.E., An Amalgam Balian-Low Theorem for symplectic lattices of rational density (2015) 2015 International Conference on Sampling Theory and Applications (SampTA), pp. 134-138. , Washington, D. C
  • Cabrelli, C., Molter, U., Pfander, G.E., Time-frequency shift invariance and the Amalgam Balian-Low theorem (2016) Appl. Comput. Harmon. Anal., 41 (3), pp. 677-691
  • Gröchenig, K., Foundations of time-frequency analysis (2001) Applied and Numerical Harmonic Analysis, , Birkhäuser
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  • Hardin, D.P., Northington, V.M.C., Powell, A.M., A sharp balian-low uncertainty principle for shift-invariant spaces (2016) Appl. Comput. Harmon. Anal.
  • Low, F., Complete sets of wave packets (1985) A Passion for Physics-Essays in Honor of Geoffrey Chew, pp. 17-22. , (edited by C. DeTar et al.), Singapore, World Scientific
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Citas:

---------- APA ----------
Cabrelli, C., Molter, U., Lee, D.G., Pfander, G.E., Anbarjafari G., Kivinukk A. & Tamberg G. (2017) . Extra invariance and Balian-Low type obstructions for Gabor spaces. 12th International Conference on Sampling Theory and Applications, SampTA 2017, 391-395.
http://dx.doi.org/10.1109/SAMPTA.2017.8024416
---------- CHICAGO ----------
Cabrelli, C., Molter, U., Lee, D.G., Pfander, G.E., Anbarjafari G., Kivinukk A., et al. "Extra invariance and Balian-Low type obstructions for Gabor spaces" . 12th International Conference on Sampling Theory and Applications, SampTA 2017 (2017) : 391-395.
http://dx.doi.org/10.1109/SAMPTA.2017.8024416
---------- MLA ----------
Cabrelli, C., Molter, U., Lee, D.G., Pfander, G.E., Anbarjafari G., Kivinukk A., et al. "Extra invariance and Balian-Low type obstructions for Gabor spaces" . 12th International Conference on Sampling Theory and Applications, SampTA 2017, 2017, pp. 391-395.
http://dx.doi.org/10.1109/SAMPTA.2017.8024416
---------- VANCOUVER ----------
Cabrelli, C., Molter, U., Lee, D.G., Pfander, G.E., Anbarjafari G., Kivinukk A., et al. Extra invariance and Balian-Low type obstructions for Gabor spaces. Int. Conf. Sampl. Theory Appl., SampTA. 2017:391-395.
http://dx.doi.org/10.1109/SAMPTA.2017.8024416