Finite Adelic Wavelet Bases and a Pseudodifferential Equation

IF 0.5 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI:10.1134/s2070046624030051

V. A. Aguilar-Arteaga, S. M. Delfín-Prieto, S. Estala-Arias

引用次数: 0

Abstract

In this article we apply a polyadic approach to obtain very explicit description of a novel kind of wavelets on the ring of finite adèles, \(\mathbb{A}_{f}\), which are also eigenfunctions of a Vladimirov-type pseudodifferential operator on \(L^2(\mathbb{A}_{f})\). As an accompaniment, we solve the Cauchy problem for a certain pseudodifferential equation.

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有限阿德利小波基与伪微分方程

摘要在这篇文章中，我们运用多子方法对有限阿代尔环 \(\mathbb{A}_{f}\)上的一种新型小波进行了非常明确的描述，这些小波也是\(L^2(\mathbb{A}_{f})\)上弗拉基米洛夫型伪微分算子的特征函数。作为补充，我们求解了某个伪微分方程的考奇问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

P-Adic Numbers Ultrametric Analysis and Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： This is a new international interdisciplinary journal which contains original articles, short communications, and reviews on progress in various areas of pure and applied mathematics related with p-adic, adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis, number theory, algebraic geometry, non-Archimedean and non-commutative geometry, theory of finite fields and rings, representation theory, functional analysis and graph theory; classical and quantum information, computer science, cryptography, image analysis, cognitive models, neural networks and bioinformatics; complex systems, dynamical systems, stochastic processes, hierarchy structures, modeling, control theory, economics and sociology; mesoscopic and nano systems, disordered and chaotic systems, spin glasses, macromolecules, molecular dynamics, biopolymers, genomics and biology; and other related fields.