Criticality for schrödinger type operators based on recurrent symmetric stable processes

Masayoshi Takeda

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let μ be a signed Radon measure on ℝ1 in the Kato class andconsider a Schrödinger type operator Hμ = (−d2/dx2)α/2 + μ on R1. Let 1 ≤ α < 2 and suppose the support of μ is compact. We then construct a bounded Hμ-harmonic function uniformly lower-bounded by a positive constant if Hμ is critical. Moreover, we show that there exists no bounded positive Hμ-harmonic function if Hμ is subcritical.

Original languageEnglish
Pages (from-to)149-167
Number of pages19
JournalTransactions of the American Mathematical Society
Volume368
Issue number1
DOIs
Publication statusPublished - 2016 Jan

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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