Vector-Valued Wavelet Packets on Local Fields of Positive Characteristic

New Zealand Journal of Mathematics

Vol. 46, (2016), Pages 9-20

Firdous A. Shah

Department of Mathematics,

University of Kashmir,

South Campus, Anantnag-192101,

Jammu and Kashmir, India.

M. Y. Bhat

Department of Mathematics,

Central University of Jammu,

Jammu-180011,

Jammu and Kashmir, India.

Abstract The concept of vector-valued multiresolution analysis on local field of positive characteristic was considered by Abdullah [Vector-valued multiresolution analysis on local fields of positive characteristic, Analysis. 34(2014) 415-428]. We construct the associated wavelet packets for such an MRA and investigate their properties by virtue of the Fourier transform. Moreover, it is shown how to obtain several new bases of the space $L^2\left(K,\mathbb C^N\right)$ by constructing a series of subspaces of these vector-valued wavelet packets.

Keywords Vector-valued multiresolution analysis, Wavelet, Wavelet packet, Local field, Fourier transform.

Classification (MSC2000) 42C40, 42C15, 43A70, 11S85.