Symbol calculus of square-integrable operator-valued maps

2012/03/28 by Ingrid Beltiţă, Beltita, I., Daniel Beltiţă +3
Mathematics · Physics and Astronomy · #22E66 #35S05 #46H30 #46K15 #46L65 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1203.6347

openalex publication_date 2012/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop an abstract framework for the investigation of quantization and dequantization procedures based on orthogonality relations that do not necessarily involve group representations. To illustrate the usefulness of our abstract method we show that it behaves well with respect to the infinite tensor products. This construction subsumes examples coming from the study of magnetic Weyl calculus, the magnetic pseudo-differential Weyl calculus, the metaplectic representation on locally compact abelian groups, irreducible representations associated with finite-dimensional coadjoint orbits of some special infinite-dimensional Lie groups, and the square-integrability properties shared by arbitrary irreducible representations of nilpotent Lie groups.

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