Paper Title:

Dyadic Riesz Wavelets on Local Fields of Positive Characteristics

Author(s):

Kartik Garg, Raj Kumar, Satyapriya

Department of Mathematics,
University of Delhi,
Delhi,
India.
kartikgarg1421@gmail.com,
rajkmc@gmail.com
kmc.satyapriya@gmail.com

 

Abstract:

In this research paper, we introduce a novel theory for the construction of a Riesz wavelet basis in the space L²(K), where K is a local field with positive characteristics. Our approach is two fold: firstly, we derive some essential characterizations of the scaling function associated with the structure of a Riesz MRA on a local field, and secondly, we review existing methods for constructing wavelet frames in L²(K). We also present a well elaborated example for a better comprehension of our theory. Due to mathematical convenience, we limit ourselves to the case of dyadic dilations only.

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