Eigenvalues in potential theory

Transmission eigenvalues in inverse scattering theory

In the past few years transmission eigenvalues have become an important area of research in inverse scattering theory with active research being undertaken in many parts of the world. Transmission eigenvalues appear in the study of scattering by inhomogeneous media and are closely related to non-scattering waves. Such eigenvalues provide information about material properties of the scattering m...

On unbounded eigenvalues in particle-transport theory

The dispersion function derived from particle-transport theory is analyzed for the specific caseof a three-term redistribution law in order to define those c > I cases for which there can be eitherone or two pairs of unbounded eigenvalues, and the elementary solutions corresponding to theunbounded eigenvalues are reported. ZusammenfassungDie Dispersions-Funktion, die vonder ...

Optimal Embeddings and Eigenvalues in Support Theory

Support theory is a methodology for bounding eigenvalues and generalized eigenvalues of matrices and matrix pencils; such bounds have been stated both in algebraic terms, and in combinatorial terms based on embeddings of the underlying graphs of the matrices. In this paper, we present a theorem that demonstrates the connection between these various bounding techniques, and also suggests a possi...

Second Order Perturbation Theory for Embedded Eigenvalues

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonia...

Inverse scattering theory and transmission eigenvalues