Results 71 to 80 of about 107 (95)
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Symplectic strata and analytic hypoellipticity
2006We review various classical results on analytic hypoellipticity for operators with double characteristics. Several examples will be discussed to motivate Treves’ conjecture. Finally we announce regularity results obtained recently.
Paulo D. Cordaro, Nicholas Hanges
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On a conjecture of Treves: analytic hypoellipticity and Poisson strata
Indiana University Mathematics Journal, 1998Dans cet article, les auteurs demontrent, en utilisant certaines bonnes estimations de type \(L^2\), des resultats d'analyticité (ou de régularité Gevrey) pour certaines classes d'opérateurs de L. Hörmander; Plus précisément: Resultat 1: L'operateur (somme de 4 carrés de champs de vecteurs): \[ P=D^2_1+ \bigl(D_2+ a(x_1,x_2,x_2) D_3\bigr)^2+ x^4_1D^2_3+
Bernardi, E., Bove, A., Tartakoff, D. S.
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Toeplitz Operators, Analytic Torsion, and the Hypoelliptic Laplacian
Letters in Mathematical Physics, 2016Toeplitz operators are specific matrix blocks of pseudo-differential operators. This survey paper aims to show that they arise in several distinct but related contexts where their properties can be efficiently used. As indicated in the title and introduction of the paper the problems considered here are the study of asymptotic analytic torsion, in ...
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On global analytic and Gevrey hypoellipticity on the torus and the Métivier inequality
Communications in Partial Differential Equations, 2016ABSTRACTWe obtain a global version in the N-dimensional torus of the Metivier inequality for analytic and Gevrey hypoellipticity, and based on it we introduce a class of globally analytic hypoelliptic operators which remain so after suitable lower order perturbations. We also introduce a new class of analytic (pseudodifferential) operators on the torus
G. Chinni, P. D. Cordaro
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The Annals of Mathematics, 1983
The authors study microlocal analytic hypoellipticity and analytic hypoellipticity for various classes of pseudodifferential operators with ''polynomial coefficients'' and multiple characteristics. For the first result, we consider operators \(P(t,D_ t,D_ y)\) acting on \({\mathcal D}'({\mathbb{R}}_{t,y}^{n_ 1+n_ 2}).\) It is assumed that P is ...
Grigis, Alain, Rothschild, Linda Preiss
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The authors study microlocal analytic hypoellipticity and analytic hypoellipticity for various classes of pseudodifferential operators with ''polynomial coefficients'' and multiple characteristics. For the first result, we consider operators \(P(t,D_ t,D_ y)\) acting on \({\mathcal D}'({\mathbb{R}}_{t,y}^{n_ 1+n_ 2}).\) It is assumed that P is ...
Grigis, Alain, Rothschild, Linda Preiss
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Nonsymplectic Strata and Germ Analytic Hypoellipticity
2011In all of the above cases, the characteristic variety for the operator has been symplectic, in fact, a symplectic manifold. This is in agreement with the spirit of Treves’ conjecture that in order to have analytic hypoellipticity, the characteristic variety and all the subsidiary Poisson strata should be symplectic.
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Hypoellipticity of systems of analytic vector fields
1989The authors approach the pointwise-hypoellipticity of an m-dimensional Frobenius Lie algebra L of an analytic complex vector field in some open subset of \({\mathbb{R}}^{m+1}\). They prove that if L is hypoelliptic at a point, then it must be analytic hypoelliptic in a full neighbourhood of the same point.
K. H. Kwon, B. C. Song
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Analytic semigroups generated by globally hypoelliptic operators
Integral Transforms and Special Functions, 2006A theorem on square roots of a sectorial hypoelliptic pseudodifferential operator is given.
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Analytic Vectors of Hypoelliptic Operators of Principal Type
American Journal of Mathematics, 1982Baouendi, M. S., Metivier, G.
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