Enhanced Symmetry of the $p$-adic Wavelets

Autor:	Dutta, Parikshit, Ghoshal, Debashis, Lala, Arindam
Rok vydání:	2018
Předmět:	Mathematical Physics High Energy Physics - Theory Physics - Data Analysis Statistics and Probability
Druh dokumentu:	Working Paper
DOI:	10.1016/j.physletb.2018.07.007
Popis:	Wavelet analysis has been extended to the $p$-adic line $\mathbb{Q}_p$. 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. Comment: 1+14 pages, 1 figure (v2: infinite dimensional enhancement suggested, title modified, affiliation added, other minor changes)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1804.00958 Zobrazit plný text záznamu View this record from Arxiv