Computing the q-Numerical Range of Differential Operators

Abstract

A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of thez Hilbert space. In this paper, we establish an approximation of the q-numerical range of bounded and unbounnded operator matrices by variational methods. Application to Schrödinger operator, Stokes operator, and Hain-Lüst operator is given.