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TMF, 2019, Volume 201, Number 3, Pages 315–336 (Mi tmf9744)  

Spaces of type $S$ and deformation quantization

M. A. Soloviev

Lebedev Physical Institute, RAS, Moscow Russia

Abstract: We study the properties of the Gelfand–Shilov spaces $S^{b_n}_{a_k}$ in the context of deformation quantization. Our main result is a characterization of their corresponding multiplier algebras with respect to a twisted convolution, which is given in terms of the inclusion relation between these algebras and the duals of the spaces of pointwise multipliers with an explicit description of these functional spaces. The proof of the inclusion theorem essentially uses the equality $S^{b_n}_{a_k}=S^{b_n}\cap S_{a_k}$.

Keywords: deformation quantization, Weyl symbol, Moyal product, multiplier algebra, Gelfand–Shilov spacedeformation quantization, Weyl symbol, Moyal product, multiplier algebra, Gelfand–Shilov space.

DOI: https://doi.org/10.4213/tmf9744

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English version:
Theoretical and Mathematical Physics, 2019, 201:3, 1682–1700

Received: 15.05.2019
Revised: 15.05.2019

Citation: M. A. Soloviev, “Spaces of type $S$ and deformation quantization”, TMF, 201:3 (2019), 315–336; Theoret. and Math. Phys., 201:3 (2019), 1682–1700

Citation in format AMSBIB
\Bibitem{Sol19}
\by M.~A.~Soloviev
\paper Spaces of type $S$ and deformation quantization
\jour TMF
\yr 2019
\vol 201
\issue 3
\pages 315--336
\mathnet{http://mi.mathnet.ru/tmf9744}
\crossref{https://doi.org/10.4213/tmf9744}
\transl
\jour Theoret. and Math. Phys.
\yr 2019
\vol 201
\issue 3
\pages 1682--1700
\crossref{https://doi.org/10.1134/S004057791912002X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077551706}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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