A Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator.
| hal.structure.identifier | Mathematics, ILTPE | |
| dc.contributor.author | GOLINSKII, Leonid | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | KUPIN, Stanislas | |
| dc.date.accessioned | 2024-04-04T02:22:45Z | |
| dc.date.available | 2024-04-04T02:22:45Z | |
| dc.date.created | 2012 | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189671 | |
| dc.description.abstractEn | This is a sequel of the article by Borichev-Golinskii-Kupin [2009], where the authors obtain Blaschke-type conditions for special classes of analytic functions in the unit disk which satisfy certain growth hypotheses. These results were applied to get Lieb-Thirring inequalities for complex compact perturbations of a selfadjoint operator with a simply connected resolvent set. The first result of the present paper is an appropriate local version of the Blaschke-type condition from Borichev-Golinskii-Kupin [2009]. We apply it to obtain a similar condition for an analytic function in a finitely connected domain of a special type. Such condition is by and large the same as a Lieb-Thirring type inequality for complex compact perturbations of a selfadjoint operator with a finite-band spectrum. A particular case of this result is the Lieb--Thirring inequality for a selfadjoint perturbation of the Schatten class of a periodic (or a finite-band) Jacobi matrix. The latter result seems to be new in such generality even in this framework. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Lieb-Thirring inequality | |
| dc.subject.en | Blaschke-type condition | |
| dc.subject.en | finite-band selfadjoint operators and their complex perturbations. | |
| dc.subject.en | finite-band selfadjoint operators and their complex perturbations | |
| dc.title.en | A Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator. | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| bordeaux.journal | Journal of Mathematical Analysis and Applications | |
| bordeaux.page | 705-712 | |
| bordeaux.volume | 389 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00781336 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00781336v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Analysis%20and%20Applications&rft.date=2012&rft.volume=389&rft.issue=2&rft.spage=705-712&rft.epage=705-712&rft.eissn=0022-247X&rft.issn=0022-247X&rft.au=GOLINSKII,%20Leonid&KUPIN,%20Stanislas&rft.genre=article |
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