Harmonic functions for recurrent symmetric α-stable processeses with non-local perturbations

2025/09/17 by Kaneharu Tsuchida, Tsuchida, Kaneharu
Mathematics · #31C25(Secondary) #60J45 (Primary) 60J76 #Advanced Mathematical Physics Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2509.13918

openalex publication_date 2025/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbf M be the recurrent symmetric (relativistic) α-stable process on \mathbb R^d. Let \mathcal H^{μ+ F} (:= \mathcal H + μ+ F) be a Schrödinger type operator with local and non-local perturbations μ and F. If μ and F satisfy suitable conditions associated with Kato class, we prove the existence of ground state for a Schrödinger type operator relating to \mathcal H^{μ+ F}. Furthermore, we prove the ground state becomes a probabilistically harmonic function of the Schrödinger operator generated by \mathcal H^{μ+ F}.

Citations

• Criticality and subcriticality of generalized Schrödinger forms with non-local perturbations

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