A general Birman–Schwinger principle and some applications

Abstract: We prove a generalized Birman–Schwinger principle in the non-self-adjoint context and provide a discussion of geometric and algebraic multiplicities of eigenvalues of the basic operator of interest (e.g., a Schrödinger operator) and the associated Birman–Schwinger operator. Specifically, we study the associated Jordan chains of generalized eigenvectors of both operators. We also relate algebraic multiplicities to the notion of the index of analytic operator-valued functions and derive a general Weinstein–Aronszajn formula for a pair of non-self-adjoint operators.

This is based on joint work with Jussi Behrndt and Tom ter Elst.

mathematical physicsspectral theory

Audience: researchers in the topic

Barry Simon's 75th Birthday Conference