# Analysis Seminars

### Analysis Seminars for this Semester

**Tuesday 6th February, 2018 **
(place: UCD
Science North 125 )
4.00pm

*Speaker:* R. Smith

*Title:* Approximation of norms in Banach spaces

**Abstract**
This talk follows on from one I gave in May 2017. Let $X$ be a Banach space
and let $\mathbf P$ be a property of norms. We say that a norm $\|\cdot\|$
on $X$ (equivalent to the original norm) can be
approximated by norms having $\mathbf P$ if,
given $\varepsilon>0$, there exists another norm
$|||\cdot|||$ on $X$ with $\mathbf P$, such that $\|x\| \leq |||x||| \leq
(1+\varepsilon)\|x\|$ for all $x \in X$. There are a number of papers in
the literature that consider the question of whether or not all
(equivalent) norms on a given space can be approximated in this way.

For a number of classes of Banach spaces $X$, including $c_0(\Gamma)$
(where $\Gamma$ is an arbitrary set), certain Orlicz spaces and Lorentz
predual spaces, and a class of $C(K)$ spaces (where $K$ comes from a class
of compact spaces having unbounded scattered height), we show that all
equivalent norms on $X$ can be approximated by $C^\infty$-smooth norms or
polyhedral norms.

This is joint work with Stanimir Troyanski, University of Murcia, Spain,
and Institute of Mathematics, Bulgarian Academy of Sciences

**Tuesday 13th February, 2018 **
(place: UCD
Science North 125 )
4.00pm

*Speaker:* A. M\"uller-Hermes (Copenhagen)

*Title:* Positive maps in quantum information theory

**Abstract**
Many problems in quantum information theory are connected to
properties of positive linear maps between matrix algebras. After a brief
introduction to some basic concepts of quantum information theory I want to
focus on the problem of entanglement distillation. I will explain how this
problem is connected to the existence problem of positive linear maps that
stay positive under taking tensor powers and that are neither completely
positive nor completely co-positive. If time permits I will outline some
constructions of interesting positive maps and how non-decomposability
arises naturally from tensorisation.

**Tuesday 20th February, 2018 **
(place: UCD
Science North 125 )
4.00pm

*Speaker:* R. Harte

*Title:* 1973 and all that

**Tuesday 27th February, 2018 **
(place: UCD
Science North 125 )
4.00pm

*Speaker:* P. Tradacete (Madrid Carlos III)

*Title:* On the least doubling constant of a metric space

**Abstract**
We will explore the question of determining the least doubling constant
among all doubling measures defined on a metric space. We will show that in
many natural instances this constant is at least 2. This is based on work
in progress with J. Soria (Barcelona).

**Tuesday 6th March, 2018 **
(place: UCD
Science North 125 )
3.00pm

*Speaker:* J. Giacomoni (Pau, France)

*Title:* Diaz Saa Inequality for $p(x)$-laplacian and applications

**Abstract**
In this talk, I will present a recent work with P. Takac. It
concerns a new extension of the well-known inequality by Diaz-Saa which in
our case, involves an anisotropic operator, such as $p(x)$-Laplacian. Our
present extension of this inequality enables us to establish several new
results on the uniqueness of solutions, comparison principles and
stabilization for some anisotropic quasilinear elliptic and parabolic
equations.

**Tuesday 13th March, 2018 **
(place: UCD
Science North 125 )
4.00pm

*Speaker:* S. Gardiner

*Title:* Universal Fourier and Taylor series

**Abstract**
It has long been known that there exist trigonometric series, the
partial sums of which possess universal approximation properties on
the unit circle. It turns out that, for most smooth functions
on the unit circle, the partial sums of the associated Fourier series,
when extended to the plane, have universal approximation properties
off the circle. There are also related results for pairs of Taylor
and Laurent series arising from functions that are holomorphic off a
Jordan curve. (This is joint work with Vassili Nestoridis and Christos Papadimitropoulos.)

**Tuesday 20th March, 2018 **
(place: UCD
Science North 125 )
4.00pm

*Speaker:* P. Mellon

*Title:* Holomorphic dynamics on bounded symmetric domains

**Abstract**
The open unit ball, $B$, of a Banach space is homogeneous if given
any two points $z,w$ in $B$, there is a biholomorphic map sending
$z$ to $w$. Such balls classify the bounded symmetric domains,
include many classical spaces and ensure a Jordan structure on the
underlying space. Let $f:B\mapsto B$ be a holomorphic fixed-point
free map. The behaviour of the sequence of iterates, $f^n=f\circ
f^{n-1}$, of $f$ is the subject of much study since the Wolff Denjoy
results for the complex disc $\Delta $ in 1926. Generally, in
infinite dimensions, $(f^n)$ does not converge, even in the Hilbert
space case. Our work therefore seeks to establish the 'location'
of accumulations points of $(f^n)$, with respect to the topology
of local uniform convergence on $B$.

This seminar will present results in this direction, using a recently
proved Wolff type theorem for infinite dimensional bounded symmetric
domains.

**Tuesday 27th March **
(place: UCD
Science North 125 )
3:00pm

*Speaker:* M. Ghergu

*Title:* Isolated singularities for semilinear elliptic systems with power-law nonlinearity

**Abstract**
We discuss the behaviour around isolated singularity for
nonnegative solutions of semilinear elliptic systems. Unlike the standard
methods available in the literature which rely on moving plane methods, we
apply several tools that pertain to free boundary problems in order to
pursue our investigation.

This talk is based on a joint work with Sunghan Kim (National University
Seoul, South Korea) and Henrik Shahgholian (KTH Stockholm).

**Tuesday 27th March **
(place: UCD
Science North 125 )
4:15pm

*Speaker:* C. Boyd

*Title:* Integral and Nuclear Polynomials on tree spaces

**Abstract**
We examine the Radon-Nikodym Property and Asplundness, in particular
their connection to integral and nuclear mappings and polynomials.
We show that the structure given to us by tree spaces provides the
ideal setting to uncover the intricacies of the relationship between
integral and nuclear polynomials.
(This is joint work with C. Poulios and M. Venkova.)

**Tuesday 10th April, 2018 **
(place: UCD
Science North 125 )
4.00pm

*Speaker:* H. Render

*Title:* Generalized Bernstein operators

**Abstract**
In this talk we discuss the existence and properties of generalized
Bernstein operators in the context of extended Chebyshev spaces.
Special analysis is given to Bernstein operators in the polynomial
setting which fix the constant function 1 and the function $x^3$
with respect to an interval $[a,b]$ containing 0.

This talk is based on a joint work with
J.M. Aldaz (Universidad Autonoma de Madrid)

**Tuesday 24th April, 2018 **
(place: UCD
Science North 125 )
4.00pm

*Speaker:* M. Golitsyna

*Title:* Overconvergent properties of Dirichlet series

**Abstract**
In this talk I will describe overconvergent properties of
Dirichlet series with regard to the behavior of their
partial sums near infinity. The results are inspired by
corresponding phenomena for Taylor series, which were
recently discovered using the notion of thinness.

## Archives

- Autumn 2017 seminars
- 2016-17 seminars
- 2015-16 seminars
- 2014-15 seminars
- 2013-14 seminars
- 2012-13 seminars
- 2011-12 seminars
- 2010-11 seminars
- 2009-10 seminars
- 2008-09 seminars
- 2007-08 seminars
- 2006-07 seminars
- 2005-06 seminars
- 2004-05 seminars
- 2003-04 seminars
- 2002-03 seminars
- 2001-02 seminars
- 2000-01 seminars
- 1999-2000 seminars
- 1998-99 seminars
- 1997-98 seminars
- 1996-97 seminars
- 1995-96 seminars
- 1994-95 seminars
- 1993-94 seminars
- 1992-93 seminars
- 1991-92 seminars
- 1990-91 seminars
- 1988-89 seminars
- 1987-88 seminars
- 1986-87 seminars
- 1985-86 seminars
- 1984-85 seminars
- 1983-84 seminars
- 1982-83 seminars
- 1981-82 seminars
- 1980-81 seminars
- 1979-80 seminars