Search results for "Pseudodifferential operators"

showing 3 items of 13 documents

Spaces of weighted symbols and weighted sobolev spaces on manifolds

1987

This paper gives an approach to pseudodifferential operators on noncompact manifolds using a suitable class of weighted symbols and Sobolev spaces introduced by H.O. Cordes on ℙ. Here, these spaces are shown to be invariant under certain changes of coordinates. It is therefore possible to transfer them to manifolds with a compatible structure.

Sobolev spacePure mathematicsClass (set theory)Transfer (group theory)Symbolic calculusPseudodifferential operatorsFredholm operatorStructure (category theory)Mathematics::Differential GeometryInvariant (mathematics)Mathematics
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Pseudodifferential operators of Beurling type and the wave front set

2008

AbstractWe investigate the action of pseudodifferential operators of Beurling type on the wave front sets. More precisely, we show that these operators are microlocal, that is, preserve or reduce wave front sets. Some consequences on micro-hypoellipticity are derived.

WavefrontPseudodifferential operatorsMathematics::Complex VariablesMathematics::Operator AlgebrasApplied MathematicsMathematical analysisWave front setMicrolocal analysisMathematics::Analysis of PDEsPseudodifferential operatorWave front setType (model theory)Mathematics::Spectral TheoryAction (physics)Set (abstract data type)UltradistributionNonlinear Sciences::Pattern Formation and SolitonsAnalysisMathematicsFront (military)Journal of Mathematical Analysis and Applications
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Quantitative Approximation Properties for the Fractional Heat Equation

2017

In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss genera…

osittaisdifferentiaaliyhtälöt0209 industrial biotechnologyClass (set theory)Control and Optimizationfractional parabolic Calderón problemPseudodifferential operatorsApplied Mathematics010102 general mathematics02 engineering and technologyType (model theory)nonlocal operators [cost of approximation]01 natural sciencesinversio-ongelmatControllabilityMathematics - Analysis of PDEsweak unique continuation [Runge approximation]020901 industrial engineering & automationFOS: MathematicsApplied mathematicsHeat equationapproksimointi0101 mathematicsMathematicsAnalysis of PDEs (math.AP)
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