The aim of this paper is to use an abstract realization of the Weyl correspondence to define functions of pseudo-differential operators. We consider operators that form a self-adjoint Banach algebra. We construct on this algebra a functional calculus with respect to functions which are defined on the Euclidean space and have a finite number of derivatives.
@article{bwmeta1.element.bwnjournal-article-bcpv53z1p79bwm,
author = {Alvarez, Josefina},
title = {The Weyl correspondence as a functional calculus},
journal = {Banach Center Publications},
volume = {51},
year = {2000},
pages = {79-88},
zbl = {1034.35167},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv53z1p79bwm}
}
Alvarez, Josefina. The Weyl correspondence as a functional calculus. Banach Center Publications, Tome 51 (2000) pp. 79-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv53z1p79bwm/
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