# Past Functional Analysis Seminar

22 January 2013
17:00
to
18:16
David Seifert
Abstract
• Functional Analysis Seminar
15 January 2013
17:00
to
18:12
Chris Heunen
Abstract
• Functional Analysis Seminar
27 November 2012
17:00
to
18:12
David Preiss
Abstract
• Functional Analysis Seminar
20 November 2012
17:00
to
18:10
Pablo Shmerkin
Abstract
• Functional Analysis Seminar
13 November 2012
17:00
to
18:15
Yuri Safarov
Abstract
• Functional Analysis Seminar
30 October 2012
17:00
to
18:23
Vesselin Petkov
Abstract
We study symmetric systems with dissipative boundary conditions. The solutions of the mixed problems for such systems are given by a contraction semigroup $V(t)f = e^{tG_b}f,\: t \geq 0$. The solutions $u = e^{tG_b}f$ with eigenfunctions $f$ of the generator $G_b$ with eigenvalues $\lambda,\: \Re \lambda < 0,$ are called asymptotically disappearing (ADS). If we have (ADS), the wave operators are not complete and the inverse back-scattering problems become complicated. We examine the spectrum of the generator $G_b$ and we show that this spectrum in the open half plane $\Re \lambda < 0$ is formed by isolated eigenvalues with finite multiplicity. The existence of (ADS) is a difficult problem. We establish the existence of (ADS) for the Maxwell system in the exterior of a sphere. We will discuss some other applications related to the existence of (ADS).
• Functional Analysis Seminar
23 October 2012
17:00
to
18:23
Abstract
Let $T_1,\dots,T_n$ be bounded linear operators on a complex Hilbert space $H$. We study the question whether it is possible to find a unit vector $x\in H$ such that $|\langle T_jx, x\rangle|$ is large for all $j$. Thus we are looking for a generalization of the well-known fact for $n = 1$ that the numerical radius $w(T)$ of a single operator T satisfies $w(T)\ge \|T\|/2$.
• Functional Analysis Seminar
29 May 2012
17:00
to
18:12
Yuri Tomilov
Abstract
• Functional Analysis Seminar
15 May 2012
17:00
to
18:10
Fritz Gesztesy
Abstract
We extend the classical trace formula connecting the trace of resolvent dif- ferences of two (not necessarily self-adjoint) operators A and A0 with the logarithmic derivative of the associated perturbation determinant from the standard case, where A and A0 have comparable domains (i.e., one contains the other) to the case where their square root domains are comparable. This is done for a class of positive-type operators A, A0. We then prove an abstract result that permits to compare square root domains and apply this to the concrete case of 2nd order elliptic partial di erential operators in divergence form on bounded Lipschitz domains. This is based on various joint work with S. Hofmann, R. Nichols, and M. Zinchenko.
• Functional Analysis Seminar