Open Access
2014 Analysis Over $C^*$-Algebras and the Oscillatory Representation
Svatopluk Krýsl
J. Geom. Symmetry Phys. 33: 1-25 (2014). DOI: 10.7546/jgsp-33-2014-1-25


Since the last two decades, several differential operators appeared in connection with the so-called oscillatory geometry. These operators act on sections of infinite rank vector bundles. Definitions of the oscillatory representation, metaplectic structure, oscillatory Dirac operator, as well as some necessary fundamental results in the analysis in $C^*$-Hilbert bundles are recalled here. These results are used for a description of the kernel of a certain second order differential operator arising from oscillatory geometry and the cohomology groups of the de Rham complex of exterior forms with values in the oscillatory representation.


Download Citation

Svatopluk Krýsl. "Analysis Over $C^*$-Algebras and the Oscillatory Representation." J. Geom. Symmetry Phys. 33 1 - 25, 2014.


Published: 2014
First available in Project Euclid: 27 May 2017

zbMATH: 1311.81159
MathSciNet: MR3222636
Digital Object Identifier: 10.7546/jgsp-33-2014-1-25

Rights: Copyright © 2014 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

Back to Top