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Content available remote The strong maximum principle for Schrödinger operators on fractals
EN
We prove a strong maximum principle for Schrödinger operators defined on a class of postcritically finite fractal sets and their blowups without boundary. Our primary interest is in weaker regularity conditions than have previously appeared in the literature; in particular we permit both the fractal Laplacian and the potential to be Radon measures on the fractal. As a consequence of our results, we establish a Harnack inequality for solutions of these operators.
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Content available remote Potential theory of Schrödinger operator based on fractional Laplacian
EN
We develop potential theory of Schrödinger operators based on fractional Laplacian on Euclidean spaces of arbitrary dimension. We focus on questions related to gaugeability and existence of q-harmonic functions. Results are obtained by analyzing properties of a symmetric α-stable Lévy process on Rd, including the recurrent case. We provide some relevant techniques and apply them to give explicit examples of gauge functions for a general class of domains.
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