Abstracts Fall  Semester 2025

Title: The Caffarelli-Silvestre extension phenomenon for complete Bernstein functions of the Laplacian 

Abstract: In their renowed paper, Caffarelli and Silvestre showed that, for 0<s<1, the fractional Laplacian (-\Delta)^s is the Dirichlet-to-Neumann operator for the differential operator div(t^{1-2s}\nabla u(x,t)) on the upper half-space.

In this talk we present a generalization of the extension techniques due to M. Kwaśnicki and J. Mucha, to the case of operators that are complete Bernstein functions of the Laplacian.