Department of Mathematics

 Analysis and Applications (AaA) Seminar at UCCS

This seminar is intended to have a very informal format, and welcomes faculty and grad students from the Pikes Peak region who are interested in contemporary research in analysis (of all sorts) and applications. Areas covered include but are not limited to real and complex analysis, functional analysis, harmonic analysis, ODEs and PDEs, mathematical physics and applications to nonlinear phenomena, numerical analysis, scientific computation and other fields (too many to enumerate). 

Fall 2017  
Fridays 2-3pm, (refreshments at 1:45pm)
ENG 101, UCCS campus

Sep 29 - Innaugural Seminar: Dr. Fritz Gesztesy, Baylor U

Oct 6 - Organizational meeting 
        Oct 13 - grad student seminar
        Oct 20 - grad student seminar
Oct 27 - Expository/Research Talk: Dr. Radu Cascaval
        Nov 3 - grad student seminar
        Nov 10 - grad student seminar: encourage attendance to the Nonlinear Days Nov 11-12;
Nov 17 - Expository/Research Talk : Dr. Oksana Bihun
        Nov 24 - Thanksgiving (no seminar)
        Dec 1 - grad student seminar
Dec 8 - Expository/Research Talk: Dr. Barbara Prinari 

Please contact Dr. Radu Cascaval (radu@uccs.edu) if you are interested to join this seminar or need more info. Limited number of parking passes will be made available to non-UCCS individuals attending this seminar.


TITLES & ABSTRACTS:

Sep 29 Seminar

Speaker: Dr. Fritz Gesztesy, Baylor University
The eigenvalue counting function for Krein-von Neumann extensions of elliptic operators  (Slides)

Abstract: We start by providing a historical introduction into the subject of Weyl-asymptotics for Laplacians on bounded domains in n-dimensional Euclidean space, and a brief introduction into the basic principles of self-adjoint extensions.

Subsequently, we turn to bounds on eigenvalue counting functions and derive such a bound for Krein-von Neumann extensions corresponding to a class of uniformly elliptic second order PDE operators (and their positive integer powers) on arbitrary open, bounded, n-dimensional subsets \Omega in R^n. (No assumptions on the boundary of \Omega are made; the coefficients are supposed to satisfy certain regularity conditions.)

Our technique relies on variational considerations exploiting the fundamental link between the Krein-von Neumann extension and an underlying abstract buckling problem, and on the distorted Fourier transform defined in terms of the eigenfunction transform of the corresponding differential operator suitably extended to all of R^n. We also consider the analogous bound for the eigenvalue counting function for the corresponding Friedrichs extension.

This is based on joint work with M. Ashbaugh, A. Laptev, M. Mitrea, and S. Sukhtaiev.

 
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