相关论文: Analytic and Gevrey Hypoellipticity for Perturbed …

For each value of k, two complex vector fields satisfying the bracket condition are exhibited the sum of whose squares is hypoelliptic but not subelliptic - in fact the operator loses k-1 derivatives in Sobolev norms. In the Appendix it is…

We construct parametrices for a class of pseudodifferential operators of infinite order acting on spaces of tempered ultradistributions of Beurling and Roumieu type. As a consequence we obtain a result of hypoellipticity in these spaces.

We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the…

This note is a comment on a recent paper by J. J. Kohn. We give an example of a second order partial differential operator, expressed as a sum of squares of complex vector fields satisfying the bracket condition, that is not hypoelliptic.

The sharp Gevrey hypoellipticity is provided for the following generalization of the M\'etivier operator, "Non-hypoellipticit\'e analytique pour $D_{x}^{2}+\left( x^{2} + y^{2}\right)D_{y}^{2}$" by G. M\'etivier, \begin{align*}…

Inspired by results of A. Bergamasco on perturbations of vector fields defined on the two-dimensional torus, and of J. Delgado and M. Ruzhansky on properties of invariant operators with respect to an elliptic operator defined on a closed…

This paper is a continuation a previous work of the authors where parametric Gevrey asymptotics for singularly perturbed nonlinear PDEs has been studied. Here, the partial differential operators are combined with particular Moebius…

We consider a periodic pseudodifferential operator $H=(-\Delta)^l+A$ ($l>0$) in $\R^d$ which satisfies the following conditions: (i) the symbol of $H$ is smooth in $x$, and (ii) the perturbation $A$ has order smaller than $2l-1$. Under…

We prove global subelliptic estimates for quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. In a previous joint work with M. Hitrik, we…

In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of…

We consider sums of squares operators globally defined on the torus. We show that if some assumptions are satisfied the operators are globally analytic hypoelliptic. The purpose of the assumptions is to rule out the existence of a Hamilton…

We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower…

We give a brief survey of recent results concerning almost diagonalization of pseudodifferential operators via Gabor frames. Moreover, we show new connections between symbols with Gevrey, analytic or ultra-analityc regularity and…

We study a class of sum of squares exhibiting the same Poisson-Treves stratification as the Oleinik-Radkevi\v{c} operator. We find three types of operators having distinct microlocal structures. For one of these we prove a Gevrey…

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for $CR$ manifolds and H\"ormander's bracket condition for real vector fields. Applications are given…

We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…

The recent example of Hanges: $P = \partial_t^2 + t^2\Delta_x + \partial^2_{\theta(x)}$ in $R^3$ is analytic hypoelliptic in the sense of germs but not in the strong sense in any neighborhood of the origin. And its characteristic variety is…

We study semiclassical Gevrey pseudodifferential operators acting on the Bargmann space of entire functions with quadratic exponential weights. Using some ideas of the time frequency analysis, we show that such operators are uniformly…

We attach representations to non-symplectic stratum in the characteristic set of real vector fields. This leads to Schrodinger operators. The analysis of the solutions of these Schrodinger equations allows us to construct smooth,…

We prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid (variable coefficient) quadratic polynomials in real vector fields satisfying the H\"ormander condition and…