Functional Analysis Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
1 November 2018
14:30
to
17:00
Sylvie Monniaux
Abstract

This is part of a meeting of the North British Functional Aanlysis Seminar.  There will be a tea break (15:30-16:00)

In a first talk, I shall recall the basic definitions and properties of ${\mathcal{H}}^\infty}$ functional calculus. I shall show how a second order problem can be reduced to a first order system and how to construct potential operators.
In a second talk, we will see how to use potential operators for the specific problem of the Stokes operator with the so-called “natural” boundary conditions in non smooth domains.
Most parts which will be presented are taken from a joint work with Alan McIntosh (to be published soon in the journal "Revista Matematica Iberoamericana”)

 

 

 

 

 

 

  • Functional Analysis Seminar
1 November 2018
17:00
David Seifert
Abstract

This talk is associated with the NBFAS meeting.

We discuss the quantitative asymptotic behaviour of operator semigroups. Batty and Duyckaerts obtained upper and lower bounds on the rate of decay of a semigroup given bounds on the resolvent growth of the semigroup generator. They conjectured that in the Hilbert space setting and for the special case of polynomial resolvent growth it is possible to improve the upper bound so as to yield the exact rate of decay up to constants. This conjecture was proved to be correct by Borichev and Tomilov, and the conclusion was extended by Batty, Chill and Tomilov to certain cases in which the resolvent growth is not exactly polynomial but almost. In this talk we extend their result by showing that one can improve the upper bound under a significantly milder assumption on the resolvent growth. This result is optimal in a certain sense. We also discuss how this improved result can be used to obtain sharper estimates on the rate of energy decay for a wave equation subject to viscoelastic damping at the boundary. The talk is based on joint work with J. Rozendaal and R. Stahn.

  • Functional Analysis Seminar
2 November 2018
09:30
Abstract

This is part of a meeting of the North British Functional Analysis Seminar.

In this talk I will present an overview on generalized square functions in Banach spaces and some of their recent uses in “Analysis in Banach Spaces”. I will introduce the notions of $R$-boundedness and $\gamma$-radonifying operators and discuss their origins and some of their applications to harmonic analysis, functional calculus, control theory, and stochastic analysis.

  • Functional Analysis Seminar
2 November 2018
11:00
Abstract

This is part of a meeting of the North British Functional Analysis Seminar

In this talk I will present some new $L_p$-$L_q$-Fourier multiplier theorems which hold for operator-valued symbols under geometric restrictions on the underlying Banach spaces such as (Fourier) (co)type. I will show how the multiplier theorems can be applied to obtain new stability results for semigroups arising in evolution equations. This is based on joint work with Jan Rozendaal (ANU, Canberra).

  • Functional Analysis Seminar
2 November 2018
12:00
Houry Melkonian
Abstract

This talk is associated with the NBFAS meeting.

Consider a periodic function f, such that its restriction to the unit segment lies in the Banach space L2 = L2(0, 1). Denote by S the family of dilations f(nx) for all n positive integer. The purpose of this talk is to discuss the following question: When does S form a Riesz basis of L2?

In this talk, we will present a new mutli-term criteria for determining Riesz basis properties of S in L2. This method relies on a general framework developed by Hedenmalm, Lindqvist and Seip about 20 years ago, which turns the basis question into one about the localisation of the zeros and poles of a corresponding analytic multiplier. Our results improve upon various criteria formulated previously, which give sufficient conditions for invertibility of the multiplier in terms of sharp estimates on the Fourier coefficients.

We will then examine the application of these criteria in the case off being the p-trigonometric functions. These functions arise naturally in the context of the non-linear eigenvalue problem associated to the one-dimensional p-Laplacian in the unit segment. These results improve upon those of Edmunds, Gurka, and Lang in 2014, and others.

  • Functional Analysis Seminar
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