Criticality for schrödinger type operators based on recurrent symmetric stable processes

Masayoshi Takeda

doi:10.1090/tran/6319

Criticality for schrödinger type operators based on recurrent symmetric stable processes

Masayoshi Takeda

SCI - Mathematics

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

4 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 language	English
Pages (from-to)	149-167
Number of pages	19
Journal	Transactions of the American Mathematical Society
Volume	368
Issue number	1
DOIs	https://doi.org/10.1090/tran/6319
Publication status	Published - 2016 Jan

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/tran/6319

Fingerprint Dive into the research topics of 'Criticality for schrödinger type operators based on recurrent symmetric stable processes'. Together they form a unique fingerprint.

Cite this

@article{a82c7ee59ec749558fea4bfc4aa768fa,

title = "Criticality for schr{\"o}dinger type operators based on recurrent symmetric stable processes",

abstract = "Let μ be a signed Radon measure on ℝ1 in the Kato class andconsider a Schr{\"o}dinger 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.",

author = "Masayoshi Takeda",

note = "Publisher Copyright: {\textcopyright} 2015 American Mathematical Society.",

year = "2016",

month = jan,

doi = "10.1090/tran/6319",

language = "English",

volume = "368",

pages = "149--167",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - Criticality for schrödinger type operators based on recurrent symmetric stable processes

AU - Takeda, Masayoshi

PY - 2016/1

Y1 - 2016/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84944768821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944768821&partnerID=8YFLogxK

U2 - 10.1090/tran/6319

DO - 10.1090/tran/6319

M3 - Article

AN - SCOPUS:84944768821

VL - 368

SP - 149

EP - 167

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -

Criticality for schrödinger type operators based on recurrent symmetric stable processes

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this