Algebraic results on rngs of singular functions

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-01-30 DOI:10.1515/forum-2023-0445

Arran Fernandez, Müge Saadetoğlu

引用次数: 0

Abstract

We consider a Mikusiński-type convolution algebra C α

{C_{\alpha}}

, including functions with power-type singularities at the origin as well as all functions continuous on [ 0 , ∞ )

{[0,\infty)}

. Algebraic properties of this space are derived, including its ideal structure, filtered and graded structure, and Jacobson radical. Applications to operators of fractional calculus and the associated integro-differential equations are discussed.

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奇异函数 rngs 的代数结果

我们考虑一个 Mikusiński- 类型的卷积代数 C α {C_{\alpha}} ，其中包括在原点具有幂型奇点的函数以及所有在 [ 0 , ∞ ) 上连续的函数。包括在原点具有幂型奇点的函数以及所有在 [ 0 , ∞ ) 上连续的函数。 {[0,\infty)}上连续的所有函数。推导了这个空间的代数性质，包括其理想结构、滤波和分级结构以及雅各布森基。讨论了分数微积分算子和相关积分微分方程的应用。

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

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.