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QUALITATIVE UNCERTAINTY PRINCIPLE FOR GABOR TRANSFORM

  • Bansal, Ashish (Department of Mathematics Keshav Mahavidyalaya (University of Delhi)) ;
  • Kumar, Ajay (Department of Mathematics University of Delhi)
  • Received : 2015.08.26
  • Published : 2017.01.31

Abstract

We discuss the qualitative uncertainty principle for Gabor transform on certain classes of the locally compact groups, like abelian groups, ${\mathbb{R}}^n{\times}K$, K ⋉ ${\mathbb{R}}^n$ where K is compact group. We shall also prove a weaker version of qualitative uncertainty principle for Gabor transform in case of compact groups.

Keywords

Acknowledgement

Supported by : University of Delhi

References

  1. A. Bansal and A. Kumar, Heisenberg uncertainty inequality for Gabor transform, J. Math. Inequal. 10 (2016), 737-749.
  2. M. Benedicks, On Fourier transforms of functions supported on sets of finite Lebesgue measure, J. Math. Anal. Appl. 106 (1985), no. 1, 180-183. https://doi.org/10.1016/0022-247X(85)90140-4
  3. G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, 1994.
  4. G. B. Folland and A. Sitaram, The uncertainty principle: a mathematical survey, J. Fourier Anal. Appl. 3 (1997), no. 3, 207-238. https://doi.org/10.1007/BF02649110
  5. A. Ghaani Farashahi and R. Kamyabi-Gol, Continuous Gabor transform for a class of non-Abelian groups, Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 4, 683-701.
  6. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I, Springer-Verlag, 1963.
  7. J. A. Hogan, A qualitative uncertainty principle for unimodular groups of type I, Trans. Amer. Math. Soc. 340 (1993), no. 2, 587-594. https://doi.org/10.1090/S0002-9947-1993-1102222-4
  8. S. Echterhoff, E. Kaniuth, and A. Kumar, A qualitative uncertainty principle for certain locally compact groups, Forum Math. 3 (1991), no. 3, 355-370.
  9. G. Kutyniok, A weak qualitative uncertainty principle for compact groups, Illinois J. Math. 47 (2003), no. 3, 709-724.
  10. T. Matolcsi and J. Szucs, Intersection des mesures spectrales conjugees, C. R. Acad. Sci. Paris Ser. A-B 277 (1973), A841-A843.
  11. E. Wilczok, New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform, Doc. Math. 5 (2000), 201-226.

Cited by

  1. Qualitative uncertainty principle for the Gabor transform on certain locally compact groups vol.9, pp.3, 2018, https://doi.org/10.1515/apam-2017-0050