Displaying similar documents to “Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials”

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.

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 2 . We also prove an estimate giving some intuition to what may happen in 3 dimensions.

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let A , B denote generic binary forms, and let 𝔲 r = ( A , B ) r denote their r -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the { 𝔲 r } . As a consequence, we show that each of the higher transvectants { 𝔲 r : r 2 } is redundant in the sense that it can be completely recovered from 𝔲 0 and 𝔲 1 . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of S L 2 -representations,...

On the Fefferman-Phong inequality

Abdesslam Boulkhemair (2008)

Annales de l’institut Fourier

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We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by n 2 + 4 + ϵ improving thus the bound 2 n + 4 + ϵ obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type S 0 , 0 0 , we show that this number is bounded by n + 4 + ϵ ; more precisely, for a non negative symbol a , the Fefferman-Phong inequality holds if x α ξ β a ( x , ξ ) are bounded for, roughly, 4 | α | + | β | n + 4 + ϵ . To obtain such results and others, we first prove an abstract result which...