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math.AP2026
A Hörmander spectral multiplier theorem for fractional Hardy operators
Konstantin Merz
We consider the fractional Laplacian with added critical or subcritical Hardy potential, called Hardy operator. We prove a Hörmander spectral multiplier theorem, i.e., the boundedn…
math.AP2026
On wave operators for Hardy operators with and without perturbations
Atsuhide Ishida, Konstantin Merz
We prove asymptotic completeness of the wave operators in time-dependent scattering theory which intertwine the ordinary or fractional Laplacian and the corresponding Hardy operato…
math.SP2026
Random Schrödinger operators on manifolds and abstract bounds for multiplier-type operators
Jean-Claude Cuenin, Konstantin Merz, Eduard Stefanescu
We study random Schrödinger operators on closed Riemannian manifolds with Anderson-type potentials. We prove high-probability spectral inclusion bounds showing that eigenvalues rem…