{"paper":{"title":"On one real basis for $L^2(Q_p)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.Kh. Bikulov, A.P. Zubarev","submitted_at":"2015-04-14T16:54:59Z","abstract_excerpt":"We construct new bases of real functions from $L^{2}\\left(B_{r}\\right)$ and from $L^{2}\\left(\\mathbb{Q}_{p}\\right)$. These functions are eigenfunctions of the $p$-adic pseudo-differential Vladimirov operator, which is defined on a compact set $B_{r}\\subset\\mathbb{Q}_{p}$ of the field of $p$-adic numbers $\\mathbb{Q}_{p}$ or, respectively, on the entire field $\\mathbb{Q}_{p}$. A relation between the basis of functions from $L^{2}\\left(\\mathbb{Q}_{p}\\right)$ and the basis of $p$-adic wavelets from $L^{2}\\left(\\mathbb{Q}_{p}\\right)$ is found. As an application, we consider the solution of the Cauc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03624","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}