Bochner-Riesz profile of anharmonic oscillator

Abstract

We investigate spectral multipliers, Bochner-Riesz means and the convergence of eigenfunction expansion corresponding to the Schrödinger operator with anharmonic potential $L=-\frac{d^2}{d{x}^2}+\left|x\right|$. We show that the Bochner-Riesz profile of this operator completely coincides with the profile of the harmonic oscillator $H=-\frac{d^2}{d{x}^2}+x^2$.

This is joint work with Peng Chen and Waldemar Hebisch