## Speaker:

Rupert Frank

## Institution:

Caltech

## Time:

Tuesday, June 4, 2019 - 3:00pm

## Host:

## Location:

RH 306

We consider the difference *f*(*H_*1)−*f*(*H_*0) for self-adjoint operators *H_*0 and *H_*1 acting in a Hilbert space. We establish a new class of estimates for the operator norm and the Schatten class norms of this difference. Our estimates utilise ideas of scattering theory and involve conditions on *H_*0 and *H_*1 in terms of the Kato smoothness. They allow for a much wider class of functions *f* (including some unbounded ones) than previously available results do. As an example we consider the case where *H_*0=−Δ and *H_*1=−Δ+*V* are the free and the perturbed Schrödinger operators in *L^*2(R^*d*), and *V* is a real-valued short range potential.

The talk is based on joint work with A. Pushnitski