Rocky Mountain Journal of Mathematics

Symbol calculus of square-integrable operator-valued maps

Ingrid Beltiţă, Daniel Beltiţă, and Marius Măntoiu

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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 infinite tensor products. This construction subsumes examples from the study of magnetic Weyl calculus, magnetic pseudo-differential Weyl calculus, metaplectic representation on locally compact abelian groups, irreducible representations associated with finite-dimensional coadjoint orbits of some special infinite-dimensional Lie groups, and square-integrability properties shared by arbitrary irreducible representations of nilpotent Lie groups.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 6 (2016), 1795-1851.

Dates
First available in Project Euclid: 4 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1483520428

Digital Object Identifier
doi:10.1216/RMJ-2016-46-6-1795

Mathematical Reviews number (MathSciNet)
MR3591262

Zentralblatt MATH identifier
1372.46052

Subjects
Primary: 46L65: Quantizations, deformations
Secondary: 22E66: Analysis on and representations of infinite-dimensional Lie groups 35S05: Pseudodifferential operators 46H30: Functional calculus in topological algebras [See also 47A60] 46K15: Hilbert algebras

Keywords
Symbol calculus Hilbert algebra Berezin-Toeplitz operator square-integrable representation

Citation

Beltiţă, Ingrid; Beltiţă, Daniel; Măntoiu, Marius. Symbol calculus of square-integrable operator-valued maps. Rocky Mountain J. Math. 46 (2016), no. 6, 1795--1851. doi:10.1216/RMJ-2016-46-6-1795. https://projecteuclid.org/euclid.rmjm/1483520428


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