Paper Title:

On the Construction of Dyadic Wavelet Frames in Local Fields of Positive Characteristic

Author(s):

Vishal Dhawan, Khalil Ahmad, Satyapriya, Raj Kumar

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

Department of Mathematics,
Al-Falah University,
Faridabad, Haryana,
India.
E-mail: kahmad49@gmail.com

Department of Mathematics,
University of Delhi, Delhi,
India.
E-mail: kmc.satyapriya@gmail.com

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

Abstract:

This paper explores the construction of dyadic wavelet frames in (L²(K)), where (K) is a local field with positive characteristic. Using frame multiresolution analysis (FMRA), we establish a systematic method for generating wavelet frames within this setting. While conventional results indicate that two functions are necessary for constructing wavelet frames, we demonstrate that under specific conditions, a single function is sufficient. By leveraging properties of local fields, we provide a detailed characterization of the refinement equation and necessary frame conditions. These results enhance the theoretical understanding of wavelet frames and open new directions for applications in harmonic analysis and signal representation over non-Archimedean fields.

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