Extremal discs and the regularity of CR mappings in higher codimension.
Abstract: We give some details on the geometry of the extremal discs for
CR manifolds of higher codimension and prove the following
analogue of Fefferman's mapping theorem. Let M and N be smooth
strictly pseudoconvex generic CR-manifolds in complex space. Let
F be a CR-homeomorphism M to N such that F together with its
inverse satisfies a Lipschitz condition with some exponent
0<a<1. Then F is smooth.
September 15, 1999
Bo Berndtsson
Leviplatta ytor och Seiberg-Wittens ekvationer.
September 22, 1999
Alexander Brudnyi, Beer-Sheva University, Israel
Matrix-valued corona theorem and topology of the maximal ideal
space of H^\infty.
September 29, 1999
Bo Berndtsson
Leviplatta ytor och Seiberg-Wittens ekvationer, forts.
October 6, 1999
Johan Karlsson
Nyare resultat om element- och värdeområden för
kedjebråk vilka är modellerade på de
s.k. regulära (inga förkunskaper om kedjebråk
behövs).
October 27, 1999
Klas Diederich, University of Wuppertal, Germany
Why are pluricomplex Green functions so useful?
Abstract: Several kinds of pluricomplex Green functions for bounded pseudoconvex
domains in Cn will be studied and estimates for them
derived. At least two important applications will be presented.
November 3, 1999
Niklas Lindholm
A necessary condition for sampling in some
generalized Fock spaces in Cn
Abstract: By estimating asymptotically the number of large (close to
one) eigenvalues of a certain Toeplitz concentration operator, we will
obtain a necessary condition for a uniformly separated sequence inCn
to be sampling in some weighted spaces of entire functions.
November 10, 1999
Niklas Lindholm
A necessary condition for sampling in some
generalized Fock spaces in Cn (cont. from last week)
December 15, 1999
Yurii Lyubarskii, NTNU, Trondheim
Approximation of subharmonic functions.
January 26, 2000
Sergey Kislyakov, St. Petersburg
Interpolation involving bianalytic functions.
February 9, 2000
Prof. Valerij Beloshapka, Moscow State University
Real manifolds in complex space: invariants, automorphisms,
classifications
Abstract: The problem of holomorphic classification of a domain in a complex
space is the problem of classification of its boundary. This boundary
is a real submanifold of a complex space. Such manifolds of
codimension one were studied by H. Poincaré, E. Cartan, N. Tanaka,
S. S. Chern, J. Moser and others. During the last 12 years there was
some progress in the study of real submanifolds of higher
codimension. One can mention a criteria of finite dimensionality of
the automorphisms groups, construction of the set of holomorphic
invariants and explicit description of the automorphisms group of
tangent quadric.
February 23, 2000
Stephane Rigat, Marseille/Sundsvall
Explicit version of the fundamental principle in the non homogeneous
case and applications to the complex Cauchy problem.
March-May, 2000
Evgenij Chirka, Moscow
Course on Selected topics in SCV.
March 1, 2000
Maria Roginskaya
On the growth of harmonic and M-harmonic functions in the complex unit
ball near the singularities on the boundary.
March 8, 2000
Roland Wolff, Sarbrücken
Composition of inner mappings on the ball.
Abstract: It is well known that the composition of two inner functions
on the unit disc in the complex plane is an inner function again.
If $F:B_k\to B_m$ and $G:B_m\to B_n$ are inner mappings on the
corresponding unit balls, then in general $G\circ F$ is not inner.
But if the Borel measure $\sigma_k^{F^\ast}$ on the sphere $S_m$,
\[
\sigma_k^{F^\ast}(A)=\sigma_k\big(
[F^\ast]^{-1}(A)
\big)
\]
satisfies $\sigma_k^{F^\ast}=\sigma_m$ (= surface measure on $S_m$),
then it was shown
by Ding and Sun in 1997 that $G\circ F$ is inner. This solves a
problem posed by Walter Rudin in 1986. In this talk an operator
theoretic approach to the problem will be presented and it will
be proved that the weaker condition $\sigma_k^{F^\ast}\ll\sigma_m$
is sufficient for $G\circ F$ to be inner.
March 15, 2000
Bruno Fabre
The Abel-Lie theorem
April 12, 2000
Evgenij Chirka, Moscow
On Lipschitz graphs which are pseudoconvex from both sides
Abstract: It is well known that a smooth real hypersurface in complex space
dividing two domains of holomorphy is foliated by complex
hypersurfaces. The problems will be discussed for Lipschitz hypersurfaces.
April 19, 2000
Mats Andersson
Two ways to construct Taylor's functional calculus for commuting
operators.
April 26, 2000
Nikolay Shirokov, St. Petersburg
A variational formula for the Bergman kernel.
May 10, 2000
Z. Slodkowski, Chicago
Canonical models for holomorphic motions.
May 17, 2000
Mihai Putinar, Santa Barbara
Spectral localization and applications.
Abstract: The first part of the seminar will be a review,
based on simple examples, of spectral localization ideas of
N. Dunford, E. Bishop and C. Foias.
The second part of the seminar will expand these ideas from
one complex variable to several complex variables, with some aid
and intuition from complex analytic geometry. Several applications
to division problems and computation of index will be discussed.