Developed a theory of ultradifferentiable sheafs with applications.
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5 results for “ultradifferentiability”
problem Ultradifferentiable functions and their sheafs.
method Abstract theory development for ultradifferentiable sheafs.
result Applications to linear PDEs, differential geometry, and CR geometry.
Chevalley theorems extended to isotropic functions on matrix spaces.
problem Extending Chevalley theorems to isotropic functions on matrix spaces.
method Proving ultradifferentiable Chevalley restriction theorems for various ultradifferentiable classes.
result Isotropic functions on symmetric matrices have ultradifferentiable regularity if and only if their diagonal restrictions do.
A systematic geometric theory for the ultradifferentiable (non-quasianalytic and quasianalytic) wavefront set similar to the well-known theory in the classic smooth and analytic setting is developed. In particular an analogue of Bony's Theorem and the invariance of the ultradifferentiable wavefront set under diffeomorp…
Uniform proof for ultradifferentiability in various classes and dimensions.
problem Generalizing ultradifferentiability conditions to multidimensional cases and infinite dimensional spaces.
method Uniform proof approach that works in all cases and dimensions, including infinite dimensional Banach spaces and convenient vector spaces.
result Characterization of ultradifferentiability for general analytic germs and functions.
On spaces of arc-smooth mapsmath.CA
The paper extends properties of smooth functions to closed sets and maps.
problem Properties of smooth functions on closed sets and maps.
method Extending properties of smooth functions to closed sets and maps, proving isomorphisms with natural topologies.
result Bornological isomorphisms of function spaces are established.