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arXiv · 2107.10228

On complex-time heat kernels of fractional Schr\"odinger operators via Phragm\'en-Lindel\"of principle

Konstantin Merz
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Abstract

We consider fractional Schr\"odinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a Phragm\'en-Lindel\"of theorem for polynomially bounded functions on the right complex half-plane. The interpolation leads to possibly nonoptimal off-diagonal bounds.

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Konstantin Merz. 2021-07-21. On complex-time heat kernels of fractional Schr\"odinger operators via Phragm\'en-Lindel\"of principle. https://doi.org/10.1007/s00028-022-00819-1

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