On complex-time heat kernels of fractional Schrödinger operators via Phragmén-Lindelöf principle
arXiv:2107.10228 · doi:10.1007/s00028-022-00819-1
Abstract
We consider fractional Schrödinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a Phragmén-Lindelöf theorem for polynomially bounded functions on the right complex half-plane. The interpolation leads to possibly nonoptimal off-diagonal bounds.
26 pages, added section on applications of obtained bounds. This is a pre-print of an article published in Journal of Evolution Equations, available online at https://doi.org/10.1007/s00028-022-00819-1