函数空间上与求值泛函和加权复合算子相关的算子泛函方程

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-11-21 DOI:10.1007/s00010-024-01137-2

Francesco Altomare

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引用次数: 0

摘要

本文讨论了一些算子泛函方程，这些方程在最近的几篇论文中已经被用来发展korovkin型收敛定理的推广和推广。证明了这类算子泛函方程虽然产生于不同的环境，但有一个共同的根。从统一集合出发，证明了这类算子泛函方程的解必然是评价泛函和加权复合算子。详细讨论了几种特殊情况，包括实线上\(2\pi -\)周期函数空间的特殊情况。

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On some operator functional equations related to evaluation functionals and weighted composition operators on function spaces

The paper is concerned with some operator functional equations which have been recently considered in several papers in developing some extensions and generalizations of Korovkin-type convergence theorems. It is shown that such operator functional equations although arising from different contexts, have a common root. Starting from an unifying setting, it is shown that the solutions of such operator functional equations are necessarily evaluation functionals and weighted composition operators, respectively. Several special cases are discussed in detail, including the one which concerns spaces of \(2\pi -\)periodic functions on the real line.

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.