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Displaying similar documents to “Traces and quasi-traces on the Boutet de Monvel algebra”

Analytic index formulas for elliptic corner operators

Boris Fedosov, Bert-Wolfgang Schulze, Nikolai Tarkhanov (2002)

Annales de l’institut Fourier

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Spaces with corner singularities, locally modelled by cones with base spaces having conical singularities, belong to the hierarchy of (pseudo-) manifolds with piecewise smooth geometry. We consider a typical case of a manifold with corners, the so-called "edged spindle", and a natural algebra of pseudodifferential operators on it with special degeneracy in the symbols, the "corner algebra". There are three levels of principal symbols in the corner algebra, namely...

Subalgebras to a Wiener type algebra of pseudo-differential operators

Joachim Toft (2001)

Annales de l’institut Fourier

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We study general continuity properties for an increasing family of Banach spaces S w p of classes for pseudo-differential symbols, where S w ∞ = S w was introduced by J. Sjöstrand in 1993. We prove that the operators in Op ( S w p ) are Schatten-von Neumann operators of order p on L 2 . We prove also that Op ( S w p ) Op ( S w r ) ⊂ Op ( S w r ) and S w p · S w q ⊂ S w r , provided 1 / p + 1 / q = 1 / r . If instead 1 / p + 1 / q = 1 + 1 / r , then S w p w * S w q ⊂ S w r . By modifying the definition of the S w p -spaces, one also obtains symbol classes related to the S ( m , g ) spaces.

Composition of some singular Fourier integral operators and estimates for restricted X -ray transforms

Allan Greenleaf, Gunther Uhlmann (1990)

Annales de l'institut Fourier

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We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations C ⊂ ( T * X ∖ 0 ) × ( T * Y ∖ 0 ) . These canonical relations, which arise naturally in integral geometry, are such that π : C → T * Y is a Whitney fold and ρ : C → T * X is a blow-down mapping. If A ∈ I m ( C ) , B ∈ I m ' ( C t ) , then B A ∈ I m + m ' , 0 ( Δ , Λ ) a class of pseudodifferential operators with singular symbols. From this follows L 2 boundedness of A with a loss of 1/4 derivative.

Microlocal regularity at the boundary for pseudo-differential operators with the transmission property (I)

Maurice De Gosson (1982)

Annales de l'institut Fourier

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This work is devoted to a systematic study of the microlocal regularity properties of pseudo-differential operators with the transmission property. We introduce a “boundary singular spectrum”, denoted ∂ W F ω ( u ) for distributions u ∈ D ' ( R + n ) , regular in the normal variable x n (thus, ∂ W F ω ( u ) = ∅ means that u ∈ ∩ s + t = 1 / 2 H s + t near the boundary), and it is shown that ∂ W F ω - m [ P ( u 0 ) x n > 0 ] is a subset of ∂ W F ( u ) if P has degree m and the transmission property. We finally prove that these results can bef used to examinate the (microlocal) regularity of the solutions...