Differentiability of spectral functions for symmetric α-stable processes

Masayoshi Takeda; Kaneharu Tsuchida

doi:10.1090/S0002-9947-07-04149-9

Differentiability of spectral functions for symmetric α-stable processes

Masayoshi Takeda, Kaneharu Tsuchida

Research output: Contribution to journal › Article › peer-review

46 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	4031-4054
Number of pages	24
Journal	Transactions of the American Mathematical Society
Volume	359
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9947-07-04149-9
Publication status	Published - 2007 Aug
Externally published	Yes

Keywords

Additive functional
Criticality
Kato measure
Spectral function
Symmetric stable process

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-07-04149-9

Cite this

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AB - 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.

KW - Additive functional

KW - Criticality

KW - Kato measure

KW - Spectral function

KW - Symmetric stable process

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Differentiability of spectral functions for symmetric α-stable processes

Abstract

Keywords

ASJC Scopus subject areas

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