Original scientific paper

https://doi.org/10.3336/gm.53.1.11

Sums of matrix-valued wave packet frames in \(L^2(ℝ^d,ℂ^{s\times r})\)

Jyoti ; Department of Mathematics, University of Delhi, Delhi-110007, India
Deepshikha ; Department of Mathematics, University of Delhi, Delhi-110007, India
Lalit K. Vashisht ; Department of Mathematics, University of Delhi, Delhi-110007, India
Geetika Verma ; Centre for Industrial and Applied Mathematics, School of Information Technology and Mathematical Sciences, University of South Australia, Adelaide, Australia

Abstract

The purpose of this paper is to first show relations between wave packet frame bounds and the scalars associated with finite sum of matrix-valued wave packet frames for the matrix-valued function space \(L^2(ℝ^d, ℂ^{s\times r}). A sufficient condition with explicit wave packet frame bounds for finite sum of matrix-valued wave packet frames in terms of scalars and frame bounds associated with the finite sum of frames is given. An optimal estimate of wave packet frame bounds for the finite sum of matrix-valued wave packet frames is presented. In the second part, we show that the rate of convergence of the frame algorithm can be increased by using frame bounds and scalars associated with the finite sum of frames. Finally, a necessary and sufficient condition for finite sum of matrix-valued wave packet frames in terms of series associated with wave packet vectors is given.

Keywords

Bessel sequence; frames; wave packet frames

Hrčak ID:

201829

URI

https://hrcak.srce.hr/201829

Publication date:

20.6.2018.

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