# The Nikos Danikas Analysis Seminar

ARISTOTLE UNIVERSITY OF THESSALONIKI
DEPARTMENT OF MATHEMATICS
DIVISION OF MATHEMATICAL ANALYSIS
Tel. 2310 997906, Fax 2310 997945

Organizing Committee:
D.Betsakos
I. Gasparis

Seminar Room: 3rd floor in the building of the School of Sciences

# Programm of Talks (2004-2005)

The seminar takes place every Tuesday 11-12 a.m. (unless otherwise stated)
This year the Seminar is dedicated to the memory of Nikos Danikas.

## Winter semester

September 28, 2004
Alfonso Montes-Rodriguez,
"The extremal behavior of Volterra operator"
Abstract: We will show that the Volterra operator
does not satisfy the Kreiss  matrix theorem
that gives a bound on the norm of the resolvent
of a matrix on finite-dimensional spaces.

October 12, 2004
Loukas Grafakos,
University of Missouri, U.S.A.
"Carleson's theorem on the a.e. convergence of Fourier series: a new approach".

October 14 (Thursday 11-12a.m.), 2004
Oscar Blasco,
University of Valencia, Spain
"Embedding theorems for spaces of analytic functions"

October 19, 2004
Antonis Bisbas,
Technological Educational Institute of West Macedonia
"Coin – tossing measures and their Fourier transforms"

October 26, 2004
No talk today because of Thessaloniki's holiday.

November 2, 2004
G. Paouris,
University of Crete
"Volume concentration on the balls of the Schatten trace class".

November 2, 2004, 12-1 p.m.
T. Carroll,
National University of Ireland, Cork
"Harmonic measure in parabola-shaped regions in $R^n$".

November 9, 2004
Ap. Giannopoulos,
University of Athens
"0-1 polytopes with many faces".

November 16, 2004
Themis Mitsis,
University of Crete
"Dimension-free bounds for the maximal function associated to convex
bodies: a new proof".

November 23, 2004
Stanislav Shkarin,
Moscow State University, Russia
"On supercyclicity and related properties of integral operators".

November 30, 2004
Matti Vuorinen,
University of Helsinki, Finland
"Teichmuller's extremal ring problem"
Abstract. An algorithmic solution to Teichm\"uller's
well-known extremal ring problem is presented. The
results are based on joint work of the speaker with Ville Heikkala.

December 14, 2004
Ioannis Platis
University of Durham, U.K.
"Complex hyperbolic Kleinian groups"

Abstract
Let $\pi_1$ be the fundamental group of a closed surface $\Sigma$ of genus $g>1$. We consider all discrete, faithful, geometrically finite and purely loxodromic representations of $\pi_1$ into ${\rm SU}(2,1)$, (the triple cover of) the group of holomorphic isometries of the complex hyperbolic space ${\bf H}^2_\C$ and we wish to trace the analytic and geometric properties of their space $\mathcal{Q_\C}$, the \textsl{complex hyperbolic quasi-Fuchsian space}. Up to now, little is known about the structure of this space and to describe it explicitely is considered one of the fundamental problems in complex hyperbolic geometry (the holy grail!). The first step towards this direction is to prove that given a discrete, faithful, geometrically finite and purely loxodromic representation $\rho_0$ of $\pi_1$, can we find an open neighbourhood of $\rho_0$ comprising representations with these properties. We show that this is indeed the case when $\rho_0$ preserves a totally real Lagrangian plane. This deduces immediately that $\mathcal{Q}_\C$ contains open sets of maximal dimension $16g-16$.

December 21, 2004
Grigoris Pavliotis
Imperial college, London, U.K.
Title: "Modulation Equations: Stochastic Bifurcation in Large Domains"
Abstract
We consider the stochastic Swift-Hohenberg equation on a large domain
near its change of stability. We show that, under the appropriate
scaling, its solutions
can be approximated by a periodic wave, which is modulated by the
solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this
approximation also extends to the invariant measures of these equations.
Joint work with D. Bloemker and M. Hairer.

January 11, 2005
Ioannis Gasparis
Aristotle University of Thessaloniki
Title: Operators on C[0,1] preserving copies of asymptotic l_1 spaces.

## Spring semester

February 15, 2005
Michel Marias
Aristotle University of Thessaloniki
Title: "Srtrongly singular multipliers on Riemannian manifolds".

February 22, 2005
Vagia Vlachou
University of Crete
Title: "Universal functions on non-simply connected domains".

March 1, 2005
No seminar today.
A meeting of the organizing committee of the
11th Panhellenic Mathematical Analysis Conference will take place.

The 11th Panhellenic Mathematical Analysis Conference will take palce in Thessaloniki in May 2006.

March 8, 2005
Andreas Tolias
University of Crete
Title: "Hereditarily indecomposable Banach spaces"

March 22, 2005
Simos Ichtiaroglou
Department of Physics, Aristotle University of Thessaloniki

March 29, 2005
Aristidis Katavolos
University of Athens
Title: "Subspaces of L_2(R) invariant by pairs of semigroups".

April 5, 2005
Georgios Eleftherakis
University of Athens
Title: "Decomposition of reflexive modules over maximal
self-adjoint abelian operator algebras".

April 12, 2005
Irene Deliyanni
Athens University of Economics and Business
Title: "Diagonal operators on hereditarily indecomposable
Banach spaces".

April 19, 2005
A. Vidras
University of Cyprus
Title: "Integral representations of analytic functions by Carleman formulae".

May 17, 2005
N. Charalambakis
Aristotle University of Thessaloniki

May 24, 2005
G. Georganopoulos
Aristotle University of Thessaloniki

Jume 28, 2005
Eva Gallardo-Gutierrez
University of Zaragoza, Spain
Title: "Composition Operators on Hardy spaces of a simply connected domain"

Abstract:

For any simply connected domain $\Omega$, we prove that a Littlewood type inequality satisfied by the symbol $\varphi$ is necessary for boundedness of the composition operator $C_{\varphi}$ on the Hardy spaces $H^p(\Omega)$, $1\leq p<\infty$, whenever the symbol $\varphi$ is finitely-valent. Of course, the corresponding "little-oh" condition held by $\varphi$ is also necessary for the compactness of $C_{\varphi}$. Nevertheless, it is shown that such inequality is not sufficient for characterizing  bounded composition operators even induced by univalent symbols. Furthermore, such inequality is no longer necessary if we drop the extra assumption on the symbol of being finitely-valent. In particular, this solves a question posed by Shapiro and Smith and shows a striking link between the geometry of the underlying domain  and the symbol inducing the composition operator in $H^p(\Omega)$, $1\leq p<\infty$.

(Joint work with María J. González y Artur Nicolau)