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Analyse relativiste. (Relativistic analysis). (French) Zbl 0629.58015

Symbolic calculus of operators in the Hilbert space of quadratic integrable solutions T of the Klein-Gordon equation \(\square T=-4m^ 2T\) is introduced. Fourier transforms of these solutions T are expressed by integrals over the sheet \(\{(m^ 2+| p|^{1/2}),p\}\subset R^{n+1}\) (where \(p\in R^ n)\) of hyperboloid which may be, however, parametrized by a ball \(| v| <c\) \((v\in R^ n)\). As a result, a calculus on this ball appears closely related to the measure \((1-c^{- 2}| v|^ 2)^{-(n+1)/2};\) the contraction \(c\to \infty\) gives the familiar Weyl symbolical calculus.
Reviewer: J.Chrastina

MSC:

58J40 Pseudodifferential and Fourier integral operators on manifolds
35L05 Wave equation
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