that is, the problem of finding a function u on M whose derivative along the flow is equal to a given function f on M . Roughly speaking, the Ccohomology of the flow is the space of non-trivial obstructions to the existence of a C solution u of (1.1) for any given function f ∈ C(M). This notion is well-defined if the range of the Lie derivative operator on the space C(M) is closed. In this case...

We prove that the approximate null-controllability with uniform cost of hypoelliptic Ornstein–Uhlenbeck equations posed on is characterized by an integral thickness geometric condition control supports. also provide associated quantitative weak observability estimates. This result for deduced from same study a large class nonautonomous elliptic moving generalize in particular results known para...

In this paper, we present necessary and sufficient conditions to have global analytic hypoellipticity for a class of first-order operators defined on $\mathbb{T}^1 \times \mathbb{S}^3$. the case real-valued coefficients, prove that an operator in is conjugated constant-coefficient satisfying Diophantine condition, such conjugation preserves hypoellipticity. where imaginary part coefficients non...

We study degenerate hypoelliptic Ornstein-Uhlenbeck operators in L spaces with respect to invariant measures. The purpose of this article is to show how recent results on general quadratic operators apply to the study of degenerate hypoelliptic Ornstein-Uhlenbeck operators. We first show that some known results about the spectral and subelliptic properties of Ornstein-Uhlenbeck operators may be...

We compute the short-time asymptotics of heat kernels for a family of hypoelliptic operators, and we relate these to the value function of an associated variational problem previously investigated in the control theory literature. These heat kernels generalize to the noncontact case a heat kernel that has been previously obtained for the contact hypoelliptic Laplacian defined on the Heisenberg ...

In this paper, we investigate the well-posedness for Cauchy problem multi-term time-fractional heat equation associated with Dunkl operator. The under consideration includes a linear combination of Caputo derivatives in time decreasing orders (0, 1) and positive constant coefficients one-dimensional operator.  To show solvability problem  use several important properties multinomial M...

We consider the path space of a manifold with measure induced by stochastic flow an infinitesimal generator that is hypoelliptic, but not elliptic. These generators can be seen as sub-Laplacians sub-Riemannian structure chosen complement. introduce concept gradient for cylindrical functionals on in such way operators are closable L2. With this place, we show bound horizontal Ricci curvature equ...