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Qualitative uncertainty principle for Gabor transform

Ajay Kumar|Ashish Bansal
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회보 (Bulletin of the KMS)|제54권 제1호|pp. 71-84

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키워드

Fourier transformqualitative uncertainty principlecontinuous Gabor transformreproducing kernel Hilbert space
주제분류수학

초록

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

Abstract

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

참고문헌 (11)

  1. A. Bansal, "Heisenberg uncertainty inequality for Gabor transform", J. Math. Inequal, 10, pp.737~749 (2016)
  2. M. Benedicks, "On Fourier transforms of functions supported on sets of finite Lebesgue measure", J. Math. Anal. Appl, 106(1), pp.180~183 (1985)
  3. G. B. Folland, "A Course in Abstract Harmonic Analysis" (1994), CRC Press
  4. G. B. Folland, "The uncertainty principle: a mathematical survey", J. Fourier Anal. Appl, 3(3), pp.207~238 (1997)
  5. A. Ghaani Farashahi, "Continuous Gabor transform for a class of non-Abelian groups", Bull. Belg. Math. Soc. Simon Stevin, 19(4), pp.683~701 (2012)
  6. E. Hewitt, "Abstract Harmonic Analysis I" (1963), Springer-Verlag
  7. J. A. Hogan, "A qualitative uncertainty principle for unimodular groups of type I", Trans. Amer. Math. Soc, 340(2), pp.587~594 (1993)
  8. S. Echterhoff, "A qualitative uncertainty principle for certain locally compact groups", Forum Math, 3(3), pp.355~370 (1991)
  9. G. Kutyniok, "A weak qualitative uncertainty principle for compact groups", Illinois J. Math, 47(3), pp.709~724 (2003)
  10. T. Matolcsi, "Intersection des mesures spectrales conjugees", C. R. Acad. Sci. Paris S´er. A-B, 277, pp.A841~A843 (1973)
  11. E. Wilczok, "New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform", Doc. Math, 5, pp.201~226 (2000)

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