Vanishing Moments of Wavelets on p-adic Fields
Athira N, Lineesh M C
TL;DR
This paper investigates the properties of wavelets on p-adic fields, focusing on vanishing moments, their computation for different wavelet types, and their relation to approximation orders and nonorthogonal wavelets.
Contribution
It introduces the concepts of p-vanishing and discrete p-vanishing moments, and explores their relationships and implications for wavelet functions on p-adic fields.
Findings
Computed p-vanishing moments for Haar-type wavelets
Established connection between p-vanishing moments and approximation order
Characterized p-vanishing moments of nonorthogonal wavelets
Abstract
A study on the vanishing moments of wavelets on p-adic fields is carried out in this paper. The p-vanishing moments and discrete p-vanishing moments are defined on a p-adic field and the relation between them is investigated. The p-vanishing moments of Haar-type and non-Haar type wavelet functions are computed. Also, the connection between p-vanishing moment of non-Haar type wavelet functions and the approximation order of the indicator function of the compact open subgroup B0 (0) of Qp are established. A characterization of the p-vanishing moments of nonorthogonal wavelets is done.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsadvanced mathematical theories