Differentiability of spectral functions for symmetric α-stable processes

Masayoshi Takeda, Kaneharu Tsuchida

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


Let μ be a signed Radon measure in the Kato class and define a Schrödinger type operator Ha;μ = 1/2 (-Δ) α/2 + a;μ on ℝd. We show that its spectral bound C(a;) =-inf σ(Ha;μ) is differentiable if α < d ≤ 2α and μ is Green-tight.

Original languageEnglish
Pages (from-to)4031-4054
Number of pages24
JournalTransactions of the American Mathematical Society
Issue number8
Publication statusPublished - 2007 Aug
Externally publishedYes


  • Additive functional
  • Criticality
  • Kato measure
  • Spectral function
  • Symmetric stable process

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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