931 research outputs found
Lifting quasianalytic mappings over invariants
Let be a rational finite dimensional
complex representation of a reductive linear algebraic group , and let
be a system of generators of the algebra of invariant
polynomials . We study the problem of lifting mappings over the mapping
of invariants . Note that
can be identified with the categorical quotient and
its points correspond bijectively to the closed orbits in . We prove that,
if belongs to a quasianalytic subclass
satisfying some mild closedness properties which guarantee resolution of
singularities in (e.g.\ the real analytic class), then admits
a lift of the same class after desingularization by local
blow-ups and local power substitutions. As a consequence we show that
itself allows for a lift which belongs to (i.e.\
special functions of bounded variation). If is a real representation of
a compact Lie group, we obtain stronger versions.Comment: 17 pages, 1 table, minor corrections, to appear in Canad. J. Mat
Regular infinite dimensional Lie groups
Regular Lie groups are infinite dimensional Lie groups with the property that
smooth curves in the Lie algebra integrate to smooth curves in the group in a
smooth way (an `evolution operator' exists). Up to now all known smooth Lie
groups are regular. We show in this paper that regular Lie groups allow to push
surprisingly far the geometry of principal bundles: parallel transport exists
and flat connections integrate to horizontal foliations as in finite
dimensions. As consequences we obtain that Lie algebra homomorphisms intergrate
to Lie group homomorphisms, if the source group is simply connected and the
image group is regular.Comment: AmSTeX, using diag.tex with fonts lams?.ps, 38 page
Differentiable perturbation of unbounded operators
If is a C^{1,\al}-curve of unbounded self-adjoint operators with
compact resolvents and common domain of definition, then the eigenvalues can be
parameterized in . If is then the eigenvalues can be
parameterized twice differentiable.Comment: amstex 9 pages. Some misprints correcte
The Convenient Setting for Quasianalytic Denjoy--Carleman Differentiable Mappings
For quasianalytic Denjoy--Carleman differentiable function classes
where the weight sequence is log-convex, stable under derivations, of
moderate growth and also an -intersection (see 1.6), we prove the
following: The category of -mappings is cartesian closed in the sense that
for convenient vector spaces.
Applications to manifolds of mappings are given: The group of
-diffeomorphisms is a regular -Lie group but not better.Comment: 29 pages. Some typos corrected; J. Functional Analysis (2011
- β¦