Displaying similar documents to “Trace theorem on the Heisenberg group”

Construction of Sobolev spaces of fractional order with sub-riemannian vector fields

Sami Mustapha, François Vigneron (2007)

Annales de l’institut Fourier

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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...

Complex vector fields and hypoelliptic partial differential operators

Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten (2010)

Annales de l’institut Fourier

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We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’s bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which...

Elementary linear algebra for advanced spectral problems

Johannes Sjöstrand, Maciej Zworski (2007)

Annales de l’institut Fourier

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We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators...

Invariant measures for the defocusing Nonlinear Schrödinger equation

Nikolay Tzvetkov (2008)

Annales de l’institut Fourier

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We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane ℝ 2 . We also prove an estimate giving some intuition to what may happen in 3 dimensions.

Semi-classical functional calculus on manifolds with ends and weighted L p estimates

Jean-Marc Bouclet (2011)

Annales de l’institut Fourier

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For a class of non compact Riemannian manifolds with ends, we give semi-classical expansions of bounded functions of the Laplacian. We then study related L p boundedness properties of these operators and show in particular that, although they are not bounded on L p in general, they are always bounded on suitable weighted L p spaces.