Operator Theory Seminar

Speaker: 
Palle Jorgensen
Topic: 
"Graph Laplacians"

Abstract:
    We study graph Laplacians, both the discrete and associated continuous variants; arising for example as limits. The setting involves a dichotomy: a distinction between (i) reproducing point values $f(x)$ for $f$ in a specified Hilbert space, as opposed to (ii)  estimation of differences $f(x) – f(y)$. In the latter case, we introduce the notion of relative reproducing kernel Hilbert space (RKHS.) The distinction between reproducing function values vs reproducing differences is made precise; and illustrated with examples from electrical network models; i.e., involving differences of function values, with differences representing measurements of voltage drop across edges in some graph. One aim is to make precise the mathematical distinctions in the analysis in the two cases, point-values vs differences. We show among other things, that every relative RKHS  on some set $X$ is canonically associated with a conditionally negative definite function on $X$.

The talk continues on April 16.

Event Date: 
April 9, 2019 - 1:30pm to 2:30pm
April 16, 2019 - 1:30pm to 2:30pm
Location: 
309 VAN
Calendar Category: 
Seminar
Seminar Category: 
Operator Theory