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Asymptotic and exact expansions of heat traces
Journal
Mathematical Physics, Analysis and Geometry
Author
Eckstein Michał
Zając Artur
Volume
18
Number
1
Article ID
28
ISSN
1385-0172
eISSN
1572-9656
Keywords in English
heat traces
asymptotic expansions
spectral theory
zeta-functions
general Dirichlet series
Language
English
Journal language
English
Abstract in English
We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are formulated in terms of the meromorphic extension of the associated spectral zeta-functions and proven to be verified for a large class of operators. We also address the problem of convergence of the obtained asymptotic expansions. General results are illustrated with a number of explicit examples.
Affiliation
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana SmoluchowskiegoWydział Matematyki i Informatyki
Scopus© citations
8
| dc.abstract.en | We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are formulated in terms of the meromorphic extension of the associated spectral zeta-functions and proven to be verified for a large class of operators. We also address the problem of convergence of the obtained asymptotic expansions. General results are illustrated with a number of explicit examples. | pl |
| dc.affiliation | Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego | pl |
| dc.affiliation | Wydział Matematyki i Informatyki | pl |
| dc.contributor.author | Eckstein, Michał - 106698 | pl |
| dc.contributor.author | Zając, Artur - 138775 | pl |
| dc.date.accessioned | 2015-12-14T14:37:24Z | |
| dc.date.available | 2015-12-14T14:37:24Z | |
| dc.date.issued | 2015 | pl |
| dc.date.openaccess | 0 | |
| dc.description.accesstime | w momencie opublikowania | |
| dc.description.number | 1 | pl |
| dc.description.publication | 2,9 | pl |
| dc.description.version | ostateczna wersja wydawcy | |
| dc.description.volume | 18 | pl |
| dc.identifier.articleid | 28 | pl |
| dc.identifier.doi | 10.1007/s11040-015-9197-2 | pl |
| dc.identifier.eissn | 1572-9656 | pl |
| dc.identifier.issn | 1385-0172 | pl |
| dc.identifier.uri | http://ruj.uj.edu.pl/xmlui/handle/item/18252 | |
| dc.language | eng | pl |
| dc.language.container | eng | pl |
| dc.rights | Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa | |
| dc.rights.licence | CC-BY | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/legalcode.pl | |
| dc.share.type | inne | |
| dc.subject.en | heat traces | pl |
| dc.subject.en | asymptotic expansions | pl |
| dc.subject.en | spectral theory | pl |
| dc.subject.en | zeta-functions | pl |
| dc.subject.en | general Dirichlet series | pl |
| dc.subtype | Article | pl |
| dc.title | Asymptotic and exact expansions of heat traces | pl |
| dc.title.journal | Mathematical Physics, Analysis and Geometry | pl |
| dc.type | JournalArticle | pl |
| dspace.entity.type | Publication |
dc.abstract.enpl
We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are formulated in terms of the meromorphic extension of the associated spectral zeta-functions and proven to be verified for a large class of operators. We also address the problem of convergence of the obtained asymptotic expansions. General results are illustrated with a number of explicit examples. dc.affiliationpl
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego dc.affiliationpl
Wydział Matematyki i Informatyki dc.contributor.authorpl
Eckstein, Michał - 106698 dc.contributor.authorpl
Zając, Artur - 138775 dc.date.accessioned
2015-12-14T14:37:24Z dc.date.available
2015-12-14T14:37:24Z dc.date.issuedpl
2015 dc.date.openaccess
0 dc.description.accesstime
w momencie opublikowania dc.description.numberpl
1 dc.description.publicationpl
2,9 dc.description.version
ostateczna wersja wydawcy dc.description.volumepl
18 dc.identifier.articleidpl
28 dc.identifier.doipl
10.1007/s11040-015-9197-2 dc.identifier.eissnpl
1572-9656 dc.identifier.issnpl
1385-0172 dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/18252 dc.languagepl
eng dc.language.containerpl
eng dc.rights
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa dc.rights.licence
CC-BY dc.rights.uri
http://creativecommons.org/licenses/by/4.0/legalcode.pl dc.share.type
inne dc.subject.enpl
heat traces dc.subject.enpl
asymptotic expansions dc.subject.enpl
spectral theory dc.subject.enpl
zeta-functions dc.subject.enpl
general Dirichlet series dc.subtypepl
Article dc.titlepl
Asymptotic and exact expansions of heat traces dc.title.journalpl
Mathematical Physics, Analysis and Geometry dc.typepl
JournalArticle dspace.entity.type
Publication Affiliations
Wydział Fizyki, Astronomii i Informatyki Stosowanej
Eckstein, Michał
Wydział Matematyki i Informatyki
Zając, Artur
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