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 language | English |
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Pages (from-to) | 149-167 |
Number of pages | 19 |
Journal | Transactions of the American Mathematical Society |
Volume | 368 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2016 Jan |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics