46 research outputs found
Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms
We present an introduction to the framework of strongly local Dirichlet forms
and discuss connections between the existence of certain generalized
eigenfunctions and spectral properties within this framework. The range of
applications is illustrated by a list of examples
A guide to the Choquard equation
We survey old and recent results dealing with the existence and properties of
solutions to the Choquard type equations and some of its variants and extensions.Comment: 39 page
A note on an upper bound of the toll of negative eigenvalues for a fractional Schrödinger operator
On radial Schrödinger operators with a Coulomb potential
International audienceThis paper presents a thorough analysis of 1-dimensional Schrödinger operators whose potential is a linear combination of the Coulomb term 1/r and the centrifugal term 1/r 2. We allow both coupling constants to be complex. Using natural boundary conditions at 0, a two parameter holomorphic family of closed operators on L 2 (R +) is introduced. We call them the Whittaker operators, since in the mathematical literature their eigenvalue equation is called the Whittaker equation. Spectral and scattering theory for Whittaker operators is studied. Whittaker operators appear in quantum mechanics as the radial part of the Schrödinger operator with a Coulomb potential