Related papers: Failure of analytic hypoellipticity in a class of …

We obtain global analytic hypoellipticity for a class of differential operators that can be expressed as a zero-order perturbation of a sum of squares of vector fields with real-analytic coefficients on compact Lie groups. The key…

In 1978 M\'etivier showed that a differential operator $P$ with analytic coefficients is elliptic if and only if the theorem of iterates holds for $P$ with respect to any non-analytic Gevrey class. In this paper we extend this theorem to…

We introduce a new approach for the study of the Problem of Iterates using the theory on general ultradifferentiable structures developed in the last years. Our framework generalizes many of the previous settings including the Gevrey case…

We analyze a general class of difference operators $H_\varepsilon = T_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon\mathbf{Z}^d)$, where $V_\varepsilon$ is a multi-well potential and $\varepsilon$ is a small parameter. We derive full…

We review the notion and the properties of the generalised \pe\ for elliptic operators in unbounded domains, and we relate it with the criticality theory. We focus on operators with almost periodic coefficients. We present a Liouville-type…

This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…

For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of the…

We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of…

We consider an operator $ P $ which is a sum of squares of vector fields with analytic coefficients. The operator has a non-symplectic characteristic manifold, but the rank of the symplectic form $ \sigma $ is not constant on $ \Char P $.…

In this paper we establish a hypoellipticity result for second order linear operators comprised by a linear combination, with infinite vanishing coefficients, of subelliptic operators in separate spaces. This generalizes previous known…

In 1980 M{\'e}tivier characterized the analytic (and Gevrey) hypoellipticity of $L^2$-solvable partial linear differential operators by a-priori estimates. In this note we extend this characterization to ultradifferentiable hypoellipticity…

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 develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(\theta, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type…

In this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups. The obtained inequalities include Hardy, Rellich, Hardy-Littllewood-Sobolev,…

We show that an obstruction of number-theoretical nature appears as a necessary condition for the global hypoellipticity of the pseudo-differential operator $L=D_t+(a+ib)(t)P(D_x)$ on $\mathbb{T}^1_t\times\mathbb{T}_x^{N}$. This condition…

In this paper, we consider periodic boundary value problems for differential equations whose coefficients are trigonometric polynomials. We construct the spaces of generalized functions, where such problems have solutions. In particular,…

This article studies the global hypoellipticity of a class of overdetermined systems of pseudo-differential operators defined on the torus. The main goal consists in establishing connections between the global hypoellipticity of the system…

We prove nonexistence results of Liouville type for nonnegative viscosity solutions of some equations involving the fully nonlinear degenerate elliptic operators ${\cal P}^\pm_k$, defined respectively as the sum of the largest and the…

We consider an arbitrary metric graph, to which we glue another graph with edges of lengths proportional to $\varepsilon$, where $\varepsilon$ is a small positive parameter. On such graph, we consider a general self-adjoint second order…

In this paper we study nonlocal equations driven by the fractional powers of hypoelliptic operators in the form $$\mathscr K u = \mathscr A u - \partial_t u \overset{def}{=} \operatorname{tr}(Q \nabla^2 u) + <BX,\nabla u> - \partial_t u,$$…