[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b150690

QUALITATIVE UNCERTAINTY PRINCIPLE FOR GABOR TRANSFORM

Bansal, Ashish (Department of Mathematics Keshav Mahavidyalaya (University of Delhi))
Kumar, Ajay (Department of Mathematics University of Delhi)

Publication Information

Bulletin of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 71-84 More about this Journal

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

qualitative uncertainty principle; Fourier transform; continuous Gabor transform; reproducing kernel Hilbert space;

Citations & Related Records

Reference

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