On WH Packets in $L^2(\mathbb{R})$

Authors

  • S. K. Kaushik Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110 007
  • Ghanshyam Singh Department of Mathematics and Statistics, University College of Science, M.L.S. University, Udaipur (Rajasthan)
  • . Virender Department of Mathematics and Statistics, University College of Science, M.L.S. University, Udaipur (Rajasthan)

DOI:

https://doi.org/10.26713/cma.v3i3.216

Keywords:

WH packets

Abstract

WH packets with respect to a Gabor system (frame) have been introduced and it has been shown with the help of examples that WH packets with respect to a Gabor frame may not be a frame for $L^2(\mathbb{R})$. A sufficient condition under which WH packets with respect to a Gabor frame is a frame for $L^2(\mathbb{R})$ has been given. A necessary and sufficient condition has also been given in this direction. Further, finite sum of Gabor frames has been considered and sufficient conditions under which finite sum of Gabor frames is a frame for $L^2(\mathbb{R})$ have been given. Finally, stability of Gabor frames has been studied and sufficient conditions in this direction have been obtained.

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References

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CITATION

How to Cite

Kaushik, S. K., Singh, G., & Virender, . (2012). On WH Packets in $L^2(\mathbb{R})$. Communications in Mathematics and Applications, 3(3), 333–344. https://doi.org/10.26713/cma.v3i3.216

Issue

Vol. 3 No. 3 (2012)

Section

Research Article

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