Abstract
AbstractFor 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.
Funder
Austrian Science Fund
Javna Agencija za Raziskovalno Dejavnost RS
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference31 articles.
1. Acatrinei, C.: Noncommutative radial waves. J. Phys. A Math. Theor. 41, 215401 (2008)
2. Acatrinei, C.: Discrete nonlocal waves. JHEP 2, 57 (2013)
3. Akhiezer, N.I.: The Classical Moment Problem and Some Related Questions in Analysis. Oliver and Boyd Ltd., Edinburgh (1965)
4. Chen, T., Fröhlich, J., Walcher, J.: The decay of unstable noncommutative solitons. Commun. Math. Phys. 237, 243–269 (2003)
5. Cuyt, A., Petersen, V.B., Verdonk, B., Waadeland, H., Jones, W.B.: Handbook of Continued Fractions for Special Functions. Springer, New York (2008)
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