Fourier integral operators and Weyl-Hörmander calculus

Jean-Michel Bony ()
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Jean-Michel Bony: Ecole Polytechnique, Centre de Mathématiques URA 169 CNRS

A chapter in New Trends in Microlocal Analysis, 1997, pp 3-21 from Springer

Abstract: Abstract It is well known that the space of classical pseudo-differential operators is invariant under conjugation by classical Fourier integral operators. However, the Weyl-Hörmander calculus [Hö1] [Hö2] provides a much larger framework for the theory of pseudo-differential operators. Any riemannian metric g on the phase space R n x × R n ξ, satisfying the conditions of definition 1.1, defines a graded algebra of pseudo-differential operators. The classical theory corresponds to a particular metric, namely g(dx,dξ) = dx 2 + dξ2/〈ξ〉2.

Keywords: Symplectic Form; Pseudodifferential Operator; Geodesic Distance; Principal Symbol; Fourier Integral Operator (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68413-8_1

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DOI: 10.1007/978-4-431-68413-8_1

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