Gelfand Triplets, Ladder Operators and Coherent States

Maria Blazquez; Manuel Gadella; Gerardo Jimenez Trejo

doi:10.20944/preprints202409.2306.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 27 September 2024 / Approved: 29 September 2024 / Online: 29 September 2024 (10:02:49 CEST)

In the present paper and inspired with a similar construction on Hermite functions, we construct two series of Gelfand triplets each one spanned by Laguerre-Gauss functions with a fixed positive value of one of their parameters, considered as the fundamental one. We prove the continuity of different types of ladder operators on these triplets. Laguerre-Gauss functions with negative value of the fundamental parameter are proven to be continuous functionals on one of these triplets. Different sorts of coherent states are considered and proven to be in some spaces of test functions corresponding to Gelfand triplets.

Gelfand triplets; Laguerre-Gauss functions; Coherent states

Physical Sciences, Mathematical Physics

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Gelfand Triplets, Ladder Operators and Coherent States

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