Enhanced symmetry of the p-adic wavelets
Abstract
Wavelet analysis has been extended to the p-adic line Qp. The p-adic wavelets are complex valued functions with compact support. As in the case of real wavelets, the construction of the basis functions is recursive, employing scaling and translation. Consequently, wavelets form a representation of the affine group generated by scaling and translation. In addition, p-adic wavelets are eigenfunctions of a pseudo-differential operator, as a result of which they turn out to have a larger symmetry group. The enhanced symmetry of the p-adic wavelets is demonstrated.
- Publication:
-
Physics Letters B
- Pub Date:
- August 2018
- DOI:
- 10.1016/j.physletb.2018.07.007
- arXiv:
- arXiv:1804.00958
- Bibcode:
- 2018PhLB..783..421D
- Keywords:
-
- Mathematical Physics;
- High Energy Physics - Theory;
- Physics - Data Analysis;
- Statistics and Probability
- E-Print:
- 1+14 pages, 1 figure (v2: infinite dimensional enhancement suggested, title modified, affiliation added, other minor changes)