Heat kernels of the discrete Laguerre operators.
Heat equation
Jacobi polynomials
Laguerre operator
Ultracontractivity
Journal
Letters in mathematical physics
ISSN: 1573-0530
Titre abrégé: Lett Math Phys
Pays: Germany
ID NLM: 101714122
Informations de publication
Date de publication:
2021
2021
Historique:
received:
30
07
2020
revised:
24
01
2021
accepted:
20
02
2021
entrez:
31
3
2021
pubmed:
1
4
2021
medline:
1
4
2021
Statut:
ppublish
Résumé
For the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the heat semigroup is ultracontractive and to compute the corresponding norms. On the one hand, this helps us to answer basic questions (recurrence, stochastic completeness) regarding the associated Markovian semigroup. On the other hand, we prove the analogs of the Cwiekel-Lieb-Rosenblum and the Bargmann estimates for perturbations of the Laguerre operators, as well as the optimal Hardy inequality.
Identifiants
pubmed: 33785981
doi: 10.1007/s11005-021-01372-7
pii: 1372
pmc: PMC7946700
doi:
Types de publication
Journal Article
Langues
eng
Pagination
32Subventions
Organisme : Austrian Science Fund FWF
ID : P 28807
Pays : Austria
Informations de copyright
© The Author(s) 2021.