# Analysis Seminar 2011-12

** Tuesday September 27th, 2011**
4.00pm
(place: TCD
2.6)

*Speaker:* R. Timoney

*Title:* Embeddings in B(H) of ideals and tensor products of JC*-triples

** Tuesday 4th October**
3.00pm
(place: UCD
Ag. 1.01)

*Speaker:* R. Harte

*Title:* Irreducible C*-algebras and Fredholm theory

** Tuesday 4th October**
4.15
(place: UCD
Ag. 1.01)

*Speaker:* C. Boyd

*Title:* Composition of completely bounded polynomials

** Tuesday 11th October**
2:30pm
(place: TCD
2.6)

*Speaker:* P. Mellon

*Title:* A Wolff theorem in Jordan context

** Tuesday 11th October**
4:00pm
(place: TCD
2.6)

*Speaker:* R. Pluta

*Title:* Lam corners in $C_0(X)$

** Tuesday 18th October**
3:00pm
(place: UCD
Ag. 1.01)

*Speaker:* O. Goubet (Amiens)

*Title:* Boundary blow up solutions for nonlinear elliptic PDE and systems

** Tuesday 18th October**
4:15pm
(place: UCD
Ag. 1.01)

*Speaker:* M. Manolaki

*Title:* Ostrowski-type theorems for harmonic functions

** Tuesday 25th October**
2:30pm
(place: TCD
2.6)

*Speaker:* D. Kitson

*Title:* Taylor-Browder spectrum on prime C*-algebras

** Tuesday 25th October**
4:00pm
(place: TCD
2.6)

*Speaker:* O. Kounchev (Bulgaria Acad Sc)

*Title:* Moment problem, cubature formulas, and Hardy spaces

** Tuesday 1st November**
2:30pm
(place: TCD
2.6)

*Speaker:* I. Gogic (Zagreb)

*Title:* Topologically finitely generated Hilbert $C(X)$-modules

** Tuesday 1st November**
4:00pm
(place: TCD
2.6)

*Speaker:* M. Mathieu (QUB)

*Title:* Spectrally bounded and spectrally isometric operators

** Tuesday 8th November**
3:00pm
(place: UCD
Ag. 1.01)

*Speaker:* P. Hoffmann

*Title:* Combinatorial properties of $(m,p)$-isometries

** Tuesday 8th November**
4:15pm
(place: UCD
Ag. 1.01)

*Speaker:* I. Todorov (QUB)

*Title:* Interactions between harmonic analysis and operator algebras

** Tuesday 15th November**
3:00pm
(place: UCD
Ag. 1.01)

*Speaker:* S. Gardiner

*Title:* Boundary behaviour of universal Taylor series

** Tuesday 15th November**
4:15pm
(place: UCD
Ag. 1.01)

*Speaker:* S. Pott (Lund)

*Title:* The multiplier algebra of product $BMO$

** Tuesday 22nd November**
2:30pm
(place: TCD
2.6)

*Speaker:* V. Burcea

*Title:* On the local hull of holomorphy of a real submanifold
in ${\mathbb C}^{N+1}$

** Tuesday 22nd November**
4:00pm
(place: TCD
2.6)

*Speaker:* R. Levene

*Title:* Schur multipliers on the hyperfinite $II_1$ factor

** Tuesday 29th November**
3:00pm
(place: UCD
Ag. 1.01)

*Speaker:* A. Brown

*Title:* The centralizer of a space of tensor products

** Tuesday 29th November**
4:15pm
(place: UCD
Ag. 1.01)

*Speaker:* S. Dineen

*Title:* Lifting holomorphic mappings

** Tuesday 6h December**
3:00pm
(place: UCD
Ag. 1.01)

*Speaker:* M. Ghergu

*Title:* Pointwise estimates for polyharmonic inequalities

** Tuesday 6h December**
4:15pm
(place: UCD
Ag. 1.01)

*Speaker:* R. Smith

*Title:* A festive look at the Szlenk index

** Tuesday 13th December, 2011**
4:00pm
(place: UCD
Ag. 1.01)

*Speaker:* R. Aron (Kent State)

*Title:* Smooth surjections without surjective restrictions

** Tuesday 24th January, 2012**
4:00pm
(place: TCD
2.6)

*Speaker:* H. Render

*Title:* Subdivision Schemes and Polyharmonic Interpolation

** 31st January**
4:00pm
(place: UCD
Ag 1.01)

*Speaker:* M. Ghergu

*Title:* Lane-Emden systems with negative exponents

** Tuesday 7th February**
4:00pm
(place: TCD
2.6)

*Speaker:* R. Timoney

*Title:* Matrix proofs for matrix inequalities?

** Tuesday 14th February**
3:00pm
(place: UCD
Ag. 1.01)

*Speaker:* L. Harris (Kentucky)

*Title:* Derivatives of bivariate polynomials, Markov's theorem and Geronimus nodes

**Abstract**
An outstanding problem that has been recently solved is
to prove V. A. Markov's theorem for derivatives of polynomials on any
real
normed linear space. An elementary argument leads to a reduction of
the
problem to a certain directional derivative on two dimensional spaces.
To
state this, let $\mathbb{P}_m(\mathbb{R}^2)$ denote the space of all polynomials
$p(s,t)$ of degree at most $m$ and let
\[
\mathbb{N}_k = \{ (\cos (n\pi/m), \cos (q\pi/m)):~n-q =k\mod 2, ~0\leq n,q
\leq m\}.
\]
Then to prove the Markov theorem it suffices to show that the maximum
of the
values $|\hat{D}^k p(1,1)(1,-1)|$ over
polynomials $p$ in $\mathbb{P}_m(\mathbb{R}^2)$ satisfying $|p(x)| \leq 1$ for
all $x$ in the set $\mathbb{N}_k$ of nodes is attained when
$p(s,t) = T_m(s)$, where
$T_m$ is the Chebyshev polynomial of degree $m$.

We consider more general sets of nodes, called Geronimus nodes, where the extremal polynomials sought are orthogonal polynomials satisfying a three-term recurrence relation with constant coefficients. For example, this includes the Chebyshev polynomials of kinds 1-4.

In the course of our discussion we obtain an explicit formula for Lagrange polynomials and a Lagrange interpolation theorem for the Geronimus nodes. We also deduce a bivariate cubature formula analogous to Gaussian quadrature.

** Tuesday 14th February**
4:15pm
(place: UCD
Ag. 1.01)

*Speaker:* M. Manolaki

*Title:* Harmonic functions with universal polynomial expansions

** Tuesday 21st February**
2:30pm
(place: TCD
2.6)

*Speaker:* D. Kitson

*Title:* Taylor spectral theory

** Tuesday 21st February**
4:00pm
(place: TCD
2.6)

*Speaker:* H. Render

*Title:* Polyharmonic interpolation

** Tuesday 28th February**
3:30pm
(place: TCD
2.6)

*Speaker:* D. McConnell

*Title:* $C_0(X)$ algebras

** Tuesday 13th March**
2:30pm
(place: TCD
2.6)

*Speaker:* D. McConnell

*Title:* Ideals of a $C_0(X)$-algebra, its multiplier algebra and the centre

** Tuesday 13th March**
4:00pm
(place: TCD
2.6)

*Speaker:* R. Harte

*Title:* On simple permanence

** Tuesday 20th March**
3:00pm
(place: UCD
Ag. 1.01)

*Speaker:* C. Boyd

*Title:* Isometry groups of spaces of weighted holomorphic Functions

** Tuesday 20th March**
4:15pm
(place: UCD
Ag. 1.01)

*Speaker:* P. Hoffmann

*Title:* $(m, p)$-isometric operator tuples on normed spaces

** Tuesday 27th March**
2:30pm
(place: TCD
2.6)

*Speaker:* M. Melgaard (DIT)

*Title:* Recent results on weakly coupled semi-linear elliptic equations with nonlocal operators

**Abstract**
Recent results, motivated by various problems in quantum mechanics, are
presented.
The proofs are sketched and their key ingredients are discussed.

** Tuesday 27th March**
4:00pm
(place: TCD
2.6)

*Speaker:* R. Levene

*Title:* 0-1 Schur multipliers

** Tuesday 3rd April**
3:00pm
(place: UCD
Ag. 1.01)

*Speaker:* S. J. Gardiner

*Title:* Coincidence of harmonic and finely harmonic functions

** Tuesday 3rd April**
4:15pm
(place: UCD
Ag. 1.01)

*Speaker:* R. Smith

*Title:* Isomorphically polyhdedral Banach spaces

** Tuesday 10th April**
2:30pm
(place: TCD
2.6)

*Speaker:* M. Mackey

*Title:* The minimax theorem

** Tuesday 10th April**
4:00pm
(place: TCD
2.6)

*Speaker:* A. Brown

*Title:* Non-homogeneous tensor norms