On Landis conjecture for positive Schrödinger operators on graphs
arxiv(2024)
Abstract
In this note we study Landis conjecture for positive Schrödinger operators
on graphs. More precisely, we give a decay criterion that ensures when ℋ-harmonic functions for a positive Schrödinger operator ℋ with potentials bounded from above by 1 are trivial. We then
specifically look at the special cases of ℤ^d and regular trees
for which we get explicit decay criterion. Moreover, we consider the fractional
analogue of Landis conjecture on ℤ^d. Our approach relies on the
discrete version of Liouville comparison principle which is also proved in this
article.
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