Sufficient conditions of local solvability for partial differential operators on spaces of Colombeau type.
Garetto, Claudia (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Displaying similar documents to “-boundedness and -compactness of a class of Fourier integral operators.”
Sufficient conditions of local solvability for partial differential operators on spaces of Colombeau type.
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In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving...
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An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators
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2000 Mathematics Subject Classification: 42B10, 43A32. In this paper we take the strip KL = [0, +∞[×[−Lπ, Lπ], where L is a positive integer. We consider, for a nonnegative real number α, two partial differential operators D and Dα on ]0, +∞[×] − Lπ, Lπ[. We associate a generalized Fourier transform Fα to the operators D and Dα. For this transform Fα, we establish an Lp − Lq − version of the Morgan's theorem under the assumption 1 ≤ p, q ≤ +∞.