Calcul de Weyl et opérateurs sous-elliptiques
Calcul pseudodifférentiel -adique
Caractérisations des opérateurs pseudo-différentiels
Casimir operators on pseudodifferential operators of several variables.
Characterization, spectral invariance and the Fredholm property of multi-quasi-elliptic operators.
Colombeau's Generalized Functions: Topological Structures; Microlocal Properties. a Simplified Point of View. Part II
Commutator characterization of periodic pseudodifferential operators.
Complex absorbing potential method for systems [Book]
Cônes symplectiques et opérateurs de Toeplitz
Construction of Sobolev spaces of fractional order with sub-riemannian vector fields
Given a smooth family of vector fields satisfying Chow-Hörmander’s condition of step 2 and a regularity assumption, we prove that the Sobolev spaces of fractional order constructed by the standard functional analysis can actually be “computed” with a simple formula involving the sub-riemannian distance.Our approach relies on a microlocal analysis of translation operators in an anisotropic context. It also involves classical estimates of the heat-kernel associated to the sub-elliptic Laplacian.
Continuité-Sobolev de certains opérateurs paradifférentiels.
L'objet de ce travail est l'étude de la continuité des opérateurs d'intégrales singulières (au sens de Calderón-Zygmund) sur les espaces de Sobolev Hs. Il complète le travail fondamental de David-Journé [6], concernant le cas s = 0, et ceux de P. G. Lemarié [10] et M. Meyer [11] concernant le cas 0 < s < 1.
Continuity of Pseudo-differential Operators on Bessel And Besov Spaces
We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.
Corner Mellin operators and reduction of orders with parameters
Cutting the loss of derivatives for solvability under condition
For a principal type pseudodifferential operator, we prove that condition implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from for any (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition doesnotimply local solvability with a loss of 1 derivative,...
Cyclic cocycles, renormalization and eta-invariants.