Paper Title:

Wavelet Frames in Higher Dimensional Sobolev Spaces

Author(s):

Raj Kumar, Manish Chauhan, and Reena

Department of Mathematics,
Kirori Mal College, University of Delhi,
New Delhi-110007,
India.
E-mail: rajkmc@gmail.com

Department of Mathematics,
University of Delhi,
New Delhi-110007,
India
E-mail: manish17102021@gmail.com

Department of Mathematics,
Hans Raj College, University of Delhi,
New Delhi-110007,
India
E-mail: reena.bhagwat29@gmail.com

Abstract:

In this paper, we present sufficient condition for the sequence of vectors to be a frame for H^s(R^d) are derived. Necessary and sufficient conditions for the sequence of vectors to be tight wavelet frames in H^s(R^d) are obtained. Further, as an application an example of tight wavelet frames for H^s(R²) as bivariate box spline over 3-direction are given.

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