The heat kernel of a Schrödinger operator with inverse square potential
| hal.structure.identifier | Tohoku University [Sendai] | |
| dc.contributor.author | ISHIGE, Kazuhiro | |
| hal.structure.identifier | Osaka Prefecture University | |
| dc.contributor.author | KABEYA, Yoshitsugu | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.created | 2016-02-01 | |
| dc.date.issued | 2017 | |
| dc.identifier.issn | 0024-6115 | |
| dc.description.abstractEn | We consider the Schrödinger operator H = −∆ + V (|x|) with radial potential V which may have singularity at 0 and a quadratic decay at infinity. First, we study the structure of positive harmonic functions of H and give their precise behavior. Second, under quite general conditions we prove an upper bound for the correspond heat kernel p(x, y, t) of the type 0 < p(x, y, t) ≤ C t − N 2 U (min{|x|, √ t})U (min{|y|, √ t}) U (√ t) 2 exp − |x − y| 2 Ct for all x, y ∈ R N and t > 0, where U is a positive harmonic function of H. Third, if U 2 is an A 2 weight on R N , then we prove a lower bound of a similar type. | |
| dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.language.iso | en | |
| dc.publisher | London Mathematical Society | |
| dc.title.en | The heat kernel of a Schrödinger operator with inverse square potential | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1602.04172 | |
| bordeaux.journal | Proceedings of the London Mathematical Society | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01273288 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01273288v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Proceedings%20of%20the%20London%20Mathematical%20Society&rft.date=2017&rft.eissn=0024-6115&rft.issn=0024-6115&rft.au=ISHIGE,%20Kazuhiro&KABEYA,%20Yoshitsugu&OUHABAZ,%20El%20Maati&rft.genre=article |
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