Paper's 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.

Paper's Title:

Construction of a Frame Multiresolution Analysis on Locally Compact Abelian Groups

Author(s):

R. Kumar and Satyapriya

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

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

Abstract:

The frame multiresolution analysis (FMRA) on locally compact Abelian groups has been studied and the results concerning classical MRA have been worked upon to obtain new results. All the necessary conditions, which need to be imposed on the scaling function φ to construct a wavelet frame via FMRA, have been summed up. This process of construction of FMRA has aptly been illustrated by sufficient examples.

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