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4 papers · 1 filter
Full Algebra of Generalized Functions and Non-Standard Asymptotic Analysis
Todor D. Todorov, Hans Vernaeve
We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions. We offer a solution to the problem of multiplication of…
Foundations of the calculus of variations in generalized function algebras
Sanja Konjik, Michael Kunzinger, Michael Oberguggenberger
We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal proble…
Microlocal Asymptotic Analysis in Algebras of Generalized Functions
Antoine Delcroix, Michael Oberguggenberger, Jean-André Marti
We introduce a new type of local and microlocal asymptotic analysis in algebras of generalized functions, based on the presheaf properties of those algebras and on the properties o…
Generalized flows and singular ODEs on differentiable manifolds
Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer +1
Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right h…