Comptes Rendus
Analyse harmonique, Systèmes dynamiques
Dynamics of semigroups generated by analytic functions of the Laplacian on Homogeneous Trees
Pratyoosh Kumar1 ; Sumit Kumar Rano1 
1 Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781039, India
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1-13.

Let Ψ be a non-constant complex-valued analytic function defined on a connected, open set containing the L p -spectrum of the Laplacian ℒ on a homogeneous tree. In this paper we give a necessary and sufficient condition for the semigroup T(t)=e tΨ(ℒ) to be chaotic on L p -spaces. We also study the chaotic dynamics of the semigroup T(t)=e t(aℒ+b) separately and obtain a sharp range of b for which T(t) is chaotic on L p -spaces. It includes some of the important semigroups such as the heat semigroup and the Schrödinger semigroup.

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DOI : 10.5802/crmath.382
Classification : 39A12, 43A85, 47D06, 47A16, 39A33
Pratyoosh Kumar 1 ; Sumit Kumar Rano 1

1 Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781039, India
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Pratyoosh Kumar and Sumit Kumar Rano},
     title = {Dynamics of semigroups generated by analytic functions of the {Laplacian} on {Homogeneous} {Trees}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1--13},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2023},
     doi = {10.5802/crmath.382},
     language = {en},
}
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Pratyoosh Kumar; Sumit Kumar Rano. Dynamics of semigroups generated by analytic functions of the Laplacian on Homogeneous Trees. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1-13. doi : 10.5802/crmath.382. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.382/

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