Sheaves of nonlinear generalized function spaces
Eduard A. Nigsch, Andreas Debrouwere
TL;DR
This paper develops a framework for constructing diffeomorphism invariant sheaves of nonlinear generalized function spaces, enabling the creation of global algebras for distributions and ultradistributions on manifolds.
Contribution
It introduces a novel framework for diffeomorphism invariant sheaves of nonlinear generalized functions, expanding the tools for analysis on manifolds.
Findings
Constructed global algebras for distributions on manifolds
Developed diffeomorphism invariant algebras for ultradistributions
Provided a unified framework for nonlinear generalized function spaces
Abstract
We provide a framework for the construction of diffeomorphism invariant sheaves of nonlinear generalized functions spaces. As an application, global algebras of generalized functions for distributions on manifolds and diffeomorphism invariant algebras of generalized functions for ultradistributions are constructed.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Mathematical Analysis and Transform Methods · Advanced Topology and Set Theory