On one real basis for L²(Q_p)

2015/04/14 by A. Kh. Bikulov, А. Х. Бикулов, A. P. Zubarev +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph) #advanced mathematical theories #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1504.03624

15 pages

arxiv created 2015/04/14 · openalex publication_date 2015/04/14 · arxiv updated 2015/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We construct new bases of real functions from L²(B_r) and from L²(ℚ_p). These functions are eigenfunctions of the p-adic pseudo-differential Vladimirov operator, which is defined on a compact set B_r⊂ℚ_p of the field of p-adic numbers ℚ_p or, respectively, on the entire field ℚ_p. A relation between the basis of functions from L²(ℚ_p) and the basis of p-adic wavelets from L²(ℚ_p) is found. As an application, we consider the solution of the Cauchy problem with the initial condition on a compact set for a pseudo-differential equation with a general pseudo-differential operator, which is diagonal in the basis constructed.

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