Open Access
Translator Disclaimer
2016 Symbol calculus of square-integrable operator-valued maps
Ingrid Beltiţă, Daniel Beltiţă, Marius Măntoiu
Rocky Mountain J. Math. 46(6): 1795-1851 (2016). DOI: 10.1216/RMJ-2016-46-6-1795


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.


Download Citation

Ingrid Beltiţă. Daniel Beltiţă. Marius Măntoiu. "Symbol calculus of square-integrable operator-valued maps." Rocky Mountain J. Math. 46 (6) 1795 - 1851, 2016.


Published: 2016
First available in Project Euclid: 4 January 2017

zbMATH: 1372.46052
MathSciNet: MR3591262
Digital Object Identifier: 10.1216/RMJ-2016-46-6-1795

Primary: 46L65
Secondary: 22E66 , 35S05 , 46H30 , 46K15

Keywords: Berezin-Toeplitz operator , Hilbert algebra , square-integrable representation , symbol calculus

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium


Vol.46 • No. 6 • 2016
Back to Top