Semi-classical analysis on H-type groups

2018/11/30 by Clotilde Fermanian Kammerer, Fermanian-Kammerer, Clotilde, Véronique Fischer +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · doi:10.48550/arxiv.1812.00056

openalex publication_date 2018/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we develop a semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consists of a pair formed by a measure defined on the product of the group and its unitary dual, and by a field of trace class positive operators acting on the Hilbert spaces of the representations. We illustrate the theory by analyzing examples, which show in particular that this semi-classical analysis takes into account the finite-dimensioned representations of the group, even though they are negligible with respect to the Plancherel measure.

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