[Vortraege] Vortragsankündigungen (KW42), Habilitation Dr. Rainer

[Danijela Radosavljevic]

  Sehr geehrte Fakultätsmitglieder,

anbei der richtiggestellte Abstract zum Vortrag im Rahmen der 
Habilitation von Dr. Armin Rainer.

Mittwoch, 20. Oktober 2010, ab 16:15 Uhr, Seminarr. Olga Taussky-Todd (C 
209), UZA 4
Mathematisches Kolloquium – Einladung zu einem Vortrag im Rahmen der 
Habilitation von
Dr. Armin Rainer: „Quasianalytic peturbation theory and the convenient 
setting for Denjoy-Carleman classes“

Abstract: At the heart of classical perturbation theory stands the study 
of the regularity of the eigenvalues and
the eigenvectors of diagonalizable linear operators. This problem, which 
has numerous applications in the
natural sciences, is intimately related to the question, how regular the 
roots of a smooth family of polynomials
can be chosen. I will give an optimal answer for quasianalytic (i.e. 
with injective Taylor homomorphisms)
families of polynomials, respectively normal matrices, based on 
resolution of singularities. Then I shall aim for
analogous results in infinite dimensions, that is, for unbounded normal 
operators with compact resolvents and
common domain of definition. This requires a differential (convenient) 
calculus for quasianalytic mappings
beyond Banach spaces, which we recently developed for (quasianalytic and 
non-quasianalytic) Denjoy-Carleman
classes. These are function spaces intermediate between real analytic 
and $C^\infty$, characterized by growth
conditions on their Taylor expansions. I will briefly present the main 
ideas.

Mit freundlichen Grüßen

Danijela Radosavljevic

Sekretariat
Institut für Mathematik
Universität Wien
Nordbergstr. 15, UZA 4
Tel: 43 1 4277 50629
Fax: 43 1 4277 9506


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