TL;DR
This paper introduces tempered ultrafunctions, a new class of functions on non-Archimedean fields, providing generalized solutions to functional equations beyond traditional functions and distributions.
Contribution
The paper defines tempered ultrafunctions and explores their properties, linking them to tempered distributions and expanding the framework of generalized solutions.
Findings
Tempered ultrafunctions relate to tempered distributions.
They provide solutions to equations lacking classical or distributional solutions.
The paper discusses peculiar properties of tempered ultrafunctions.
Abstract
Ultrafunctions are a particular class of functions defined on some non- Archimedean field. They provide generalized solutions to functional equa- tions which do not have any solutions among the real functions or the distributions. In this paper we introduce a new class of ultrafunctions, called tempered ultrafunctions, which are somewhat related to the tem- pered distributions and present some interesting peculiarities.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Computability, Logic, AI Algorithms · Advanced Topology and Set Theory