4 papers
Propagators in curved spacetimes from operator theory
Jan Dereziński, Christian Gaß
We discuss two distinct operator-theoretic settings useful for describing (or defining) propagators associated with a scalar Klein-Gordon field on a Lorentzian manifold . Typica…
Confluent functions, Laguerre polynomials and their (generalized) bilinear integrals
Jan Dereziński, Christian Gaß, Joonas Mikael Vättö
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent o…
Point potentials on Euclidean space, hyperbolic space and sphere in any dimension
Jan Dereziński, Christian Gaß, Błażej Ruba
In dimensions d= 1, 2, 3 the Laplacian can be perturbed by a point potential. In higher dimensions the Laplacian with a point potential cannot be defined as a self-adjoint operator…
Generalized integrals and point interactions
Jan Dereziński, Christian Gaß, Błażej Ruba
First we recall a method of computing scalar products of eigenfunctions of a Sturm-Liouville operator. This method is then applied to Macdonald and Gegenbauer functions, which are…