Ultraregular generalized functions
Khaled Benmeriem, Chikh Bouzar
TL;DR
This paper introduces algebras of ultradifferentiable generalized functions and explores their microlocal analysis related to regularity and ultradifferentiability properties.
Contribution
It presents a novel framework for ultradifferentiable generalized functions and develops microlocal analysis within these algebras.
Findings
New algebraic structures for ultradifferentiable functions
Microlocal analysis tailored to ultradifferentiability
Enhanced understanding of regularity in generalized functions
Abstract
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Mathematical Analysis and Transform Methods · Iterative Methods for Nonlinear Equations