The Weyl correspondence as a functional calculus

Josefina Alvarez

Banach Center Publications (2000)

  • Volume: 53, Issue: 1, page 79-88
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Alvarez, Josefina. "The Weyl correspondence as a functional calculus." Banach Center Publications 53.1 (2000): 79-88. <http://eudml.org/doc/209079>.

@article{Alvarez2000,
abstract = {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.},
author = {Alvarez, Josefina},
journal = {Banach Center Publications},
keywords = {Weyl correspondence; functions of pseudo-differential operators; self-adjoint Banach algebra},
language = {eng},
number = {1},
pages = {79-88},
title = {The Weyl correspondence as a functional calculus},
url = {http://eudml.org/doc/209079},
volume = {53},
year = {2000},
}

TY - JOUR
AU - Alvarez, Josefina
TI - The Weyl correspondence as a functional calculus
JO - Banach Center Publications
PY - 2000
VL - 53
IS - 1
SP - 79
EP - 88
AB - 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.
LA - eng
KW - Weyl correspondence; functions of pseudo-differential operators; self-adjoint Banach algebra
UR - http://eudml.org/doc/209079
ER -

References

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  3. [3] J. Alvarez, An algebra of L p -bounded pseudo-differential operators, J. Math. Anal. Appl. 84 (1983) 268-282. Zbl0519.35084
  4. [4] J. Alvarez and A. P. Calderón, Functional calculi for pseudo-differential operators, II, in: Studies in Applied Mathematics, edited by Victor Guillemin, Academic Press, New York, 1983, 27-72. 
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  19. [19] J. C. T. Pool, Mathematical aspects of the Weyl correspondence, J. Math. Physics 7 (1966) 66-76. Zbl0139.45903
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