196,039 research outputs found
ANALYTIC HYPOELLIPTICITY for SUMS of SQUARES in the PRESENCE of SYMPLECTIC NON TREVES STRATA
No full textIn Albano, Bove and Mughetti [J. Funct. Anal. 274(10) (2018), 2725-2753]; Bove and Mughetti [Anal. PDE 10(7) (2017), 1613-1635] it was shown that Treves conjecture for the real analytic hypoellipticity of sums of squares operators does not hold. Models were proposed where the critical points causing a non-analytic regularity might be interpreted as strata. We stress that up to now there is no notion of stratum which could replace the original Treves stratum. In the proposed models such 'strata' were non-symplectic analytic submanifolds of the characteristic variety. In this note we modify one of those models in such a way that the critical points are a symplectic submanifold of the characteristic variety while still not being a Treves stratum. We show that the operator is analytic hypoelliptic
Weyl calculus for a class of subelliptic operators
No full textWeyl-Hörmander calculus is used to get a parametrix in OPS 1/2.1/21-m(Ω) for a class of subelliptic pseudodifferential operators in OPS1.0m(Ω) with real nonnegative principal symbol
An interpolation problem in the Denjoy–Carleman classes
No full textInspired by some iterative algorithms useful for proving the real analyticity (or the Gevrey regularity) of a solution of a linear partial differential equation with real-analytic coefficients, we consider the following question. Given a smooth function defined on [a,b]subset of R and given an increasing divergent sequence dn of positive integers such that the derivative of order dn of f has a growth of the type Mdn, when can we deduce that f is a function in the Denjoy-Carleman class CM([a,b])C<^>M([a,b])? We provide a positive result and show that a suitable condition on the gaps between the terms of the sequence dn is needed
On the positive parts of second order symmetric pseudo-differential operators
No full textUsing microlocalization, the positive and the negative parts for a class of second order formally self-adjoint pseudodifferetial operators are constructe
On the Cauchy Problem for a Class of Linear Weakly Hyperbolic Operators
No full textWe study a class of linear weakly hyperbolic operators with anisotropic degeneracy on their characteristic manifold and we give sufficient conditions for the well-posedness of the related Cauchy problem
Gevrey regularity for a class of sums of squares of monomial vector fields
No full textAnalytic or Gevrey hypoellipticity is proved for a class of sums of squares of vector fields having a symplectic characteristic manifold of dimension 2 and arbitrary (even) codimension. We note that this class contains examples for which the Treves stratification seems to work as well as examples for which the Treves stratification does not identify properly the non symplectic stratum
Parametrix construction for a class of anisotropic operators
No full textWe set Boutet de Monvel's Calculus for hypoelliptic operators (in the case of flat symplectic characteristic manifold) in a Weyl-Hörmander framework that also contains anisotropically vanishing symbols. In this context we construct a parametrix for the related operators. © 2003 Università degli Studi di Ferrara
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