Past Functional Analysis Seminar

8 November 2016
17:00
Alexander Pushnitski
Abstract


I will report on the results of my recent work with Dmitri Yafaev (Univeristy of Rennes-1). We consider functions $\omega$ on the unit circle with a finite number of logarithmic singularities. We study the approximation of $\omega$ by rational functions in the BMO norm. We find explicitly the leading term of the asymptotics of the distance in the BMO norm between $\omega$ and the set of rational functions of degree $n$ as $n$ goes to infinity. Our approach relies on the Adamyan-Arov-Krein theorem and on the study of the asymptotic behaviour of singular values of Hankel operators.
 

  • Functional Analysis Seminar
18 October 2016
17:00
Abstract

The talk will be a survey of recent work on the connections between group operator systems and non-signalling correlations. I will show how tensor products in the operator system category can be interpreted as physical theories, and will exhibit a refinement of non-signalling corrections giving rise to quantum attributes of graphs, including quantum versions of the chromatic and the fractional chromatic number. Relations between the parameters will be examined and further directions will be discussed.

  • Functional Analysis Seminar
7 June 2016
17:00
Jan Rozendaal (in Warsaw)
Abstract
Although much of the theory of Fourier multipliers has focused on the $(L^{p},L^{p})$-boundedness
 of such operators, for many applications it suffices that a Fourier multiplier operator is bounded
 from $L^{p}$ to $L^{q}$ with p and q not necessarily equal. Moreover, one can derive 
(L^{p},L^{q})-boundedness results for $p\neq q$ under different, and often weaker, assumptions
 than in the case $p=q$. In this talk I will explain some recent results on the
 $(L^{p},L^{q})$-boundedness of operator-valued Fourier multipliers. Also, I will sketch some
 applications to the stability theory for $C_{0}$-semigroups and functional calculus theory. 

 

This talk will be transmitted from Warsaw to us and Dresden, provided that Warsaw get things set up.  We will not be using the TCC facility,

so the location will be C1.

  • Functional Analysis Seminar
10 May 2016
17:00
Kun-Peng Jin
Abstract

We consider a system of coupled second order integro-differential evolution equations in a Hilbert space, which is partially damped through memory effects. A global existence theorem regarding the solutions to its Cauchy problem is given, only under basic conditions that the memory kernels possess positive definite primitives but without nonnegative/decreasing assumptions. Following this, we find an approach to successfully obtain the stability of the system energy and various decay rates. Moreover, the abstract results are applied to several concrete systems in the real world, including the Timoshenko type. This is a joint work with Professor Ti-Jun Xiao (Fudan University) and Professor Jin Liang (Shanghai Jiaotong University)

  • Functional Analysis Seminar

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