[Seminar] "Bernstein functional calculus and a generalized Helmholtz problem" by Prof. Daniel Hauer
Date
Location
Description
Geometric PDE and Applied Analysis Seminar (January 25, 2024)
Title: Bernstein functional calculus and a generalized Helmholtz problem
Speaker: Prof. Daniel Hauer (University of Sydney)
Abstract:
In this talk, I aim to characterize all distributional solutions of the generalized Helmholtz equation
f(−Δ)u=f(k2)u
on the Euclidean space Rd for every real k≠0 and a non-constant Berstein function f. Note, that f(−Δ) is a non-local operator and the prototype would be the fractional operator (−Δ)s for 0<s<1. To attack this problem, we first need to introduce a notion of distributional solutions of the generalized Helmholtz equation. This involves showing that the negative Laplacian is non-negative on a Lizorkin space.
The results presented in this talk are obtained in joint work with Robert Denk (University of Konstanz, Germany) and David Lee (Laboratoire Jacques-Louis Lions, Paris, France).
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