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SEMINARIO DI ANALISI ARMONICA
lunedì 26 marzo 2007
ore 15.00
Scuola Normale Superiore
Pisa
(Aula Mancini)
Peter Sjögren
Chalmers University, Göteborg
Terrà un seminario dal titolo:
"Sull'operatore massimale per certe funzioni di Laguerre"
Tutti gli interessati sono invitati a partecipare.
La Segreteria della
Classe di Scienze
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SEMINARIO DI SISTEMI DINAMICI OLOMORFI (e dintorni)
Centro di Ricerca Matematica De Giorgi
Sala Conferenze
Lunedi' 19 marzo,
---> ore 14.30 <---
Carlo Carminati (Pisa)
"Linearization of germs: regular dependence on the multiplier"
(abstarct in coda)
%%%%%%%%%%%%%%%%%%%
% Prossimamente %
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SEMINARIO DI SISTEMI DINAMICI OLOMORFI (e dintorni)
Centro di Ricerca Matematica De Giorgi
Sala Conferenze
Lunedi' 26 marzo,
---> ore 14.30 <---
Jasmin Raissy (Pisa)
"Linearization of holomorphic germs with quasi-elliptic fixed points"
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ABSTRACT.1 - 19 marzo. [joint work with S. Marmi]
We prove that the linearization of germs of holomorphic (or formal) maps with a fixed point
in one complex dimension have a ${\cal C}^1$--holomorphic dependence on the multiplier $\lambda$.
%
The linearization is analytic for $\lambda\in{\mathbb P}^1\C\setminus{\mathbb S}^1$,
the unit circle~$\Su$ appears as a natural boundary (because of resonances, i.e. roots of unity),
but the solutions are still defined at points of~${\mathbb S}^1$ which lie ``far enough from resonances'',
i.e.\ when the multiplier satisfies a suitable arithmetical condition.
We construct an increasing sequence of compacts which avoid resonances and prove that the linearization
belongs to the associated space of ${\cal C}^1$--holomorphic functions. These are a special case of Borel's
uniform monogenic functions, and their space is arcwise-quasianalytic \cite{MS2}.
Among the consequences of these results, we can prove that
the linearizations are defined and admit asymptotic expansions of Gevrey type at the points of~${\mathbb S}^1$
which satisfy a uniform version of the Brjuno condition first introduced in \cite{Ris}.
The regular dependence on the multiplier holds also in the formal ultradifferentiable case considered in \cite{CM}.}
ABSTRACT.2 - 26 marzo
> "Linearization of holomorphic germs with quasi-elliptic fixed points"
>
> Abstract: Let f be a germ of holomorphic diffeomorphism of \C^n
> with the origin O as quasi-elliptic fixed point, i.e., so that the
> spectrum of df_O contains 0 < s eigenvalues satisfying a Brjuno
> condition. We shall give sufficient conditions for the holomorphic
> linearization of f valid even when s< n.
>
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