Non-Archimedean Kelvin Transformation
Alexandra V. Antoniouk, Anatoly N. Kochubei
TL;DR
This paper introduces a non-Archimedean analog of the Kelvin transformation related to the Vladimirov-Taibleson operator on functions over non-Archimedean local fields, expanding classical harmonic analysis tools.
Contribution
It develops a new non-Archimedean Kelvin transformation associated with the Vladimirov-Taibleson operator, bridging classical and non-Archimedean harmonic analysis.
Findings
Defined the non-Archimedean Kelvin transformation.
Established properties analogous to the classical case.
Explored applications to non-Archimedean harmonic analysis.
Abstract
We introduce and study an analog of the Kelvin transformation connected with the Vladimirov-Taibleson operator acting on real- or complex-valued functions on a space over a non-Archimedean local field .
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Taxonomy
Topicsadvanced mathematical theories · Mathematical and Theoretical Analysis · Algebraic and Geometric Analysis