Sheafs of ultradifferentiable functions
Stefan F\"urd\"os
TL;DR
This paper develops a comprehensive abstract theory of ultradifferentiable sheafs and explores their applications in linear PDEs, differential geometry, and CR geometry.
Contribution
It introduces a new abstract framework for ultradifferentiable sheafs and applies it to multiple areas in mathematics, expanding the theoretical understanding.
Findings
Established a general theory of ultradifferentiable sheafs
Applied the theory to linear partial differential equations
Discussed implications for CR geometry
Abstract
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Nonlinear Differential Equations Analysis