arXiv subjects
Publications and source records attributed to Prasadini Mahapatra.
We construct the spectrum for a shift invariant space on Vilenkin group. We prove the results related to spectrum and Frame multiresolution analysis for Cantor dyadic group and Vilenkin group.
We study the properties based on the space generated by the translates of square integrable function using C-bracket on Vilenkin group. We give the necessary and sufficient condition for frame sequences by the family of translates of the function.
Vilenkin groups, introduced by F. Ya Vilenkin, form a class of locally compact abelian groups. The present paper consists of the characterization of Parseval frame multiwavelets associated to multiresolution analysis (MRA) in the Vilenkin group. Further, we introduce the pseudo-scaling function along with a class of generalized low pass filters and study their properties in Vilenkin group.
W. C. Lang determined wavelets on Cantor dyadic group by using Multiresolution analysis method. In this paper we have given characterization of wavelet sets on Cantor dyadic group providing another method for the construction of wavelets. All the wavelets originating from wavelet sets are not necessarily associated with a multiresolution analysis. Relation between multiresolution analysis and, wavelets determined from wavelet sets is established along with relevant examples.
For Vilenkin group only the existence of multiwavelets associated with multiresolution analysis (MRA) is known. In this paper, we have shown that by using wavelet sets we can also construct single wavelet in case of Vilenkin group which are not associated with MRA.We have given characterization of single and multi-wavelet sets on Vilenkin group. Further, we have studied generalized scaling sets, some of their properties and relation between wavelet sets and generalized scaling sets.