Related papers: Intrinsic Taylor formula for non-homogeneous Kolmo…
We consider a class of ultra-parabolic Kolmogorov-type operators satisfying the Hormander's condition. We prove an intrinsic Taylor formula with global and local bounds for the remainder given in terms of the norm in the homogeneous Lie…
We prove a real interpolation characterization for some non Euclidean H\"older spaces, built on the Lie structure induced by a class of ultra-parabolic Kolmogorov-type operators satisfying the H\"ormander condition. As a by-product we also…
We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak H\"ormander condition. We prove continuous embeddings into Lorentz and intrinsic H\"older spaces. We also prove…
In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operators form a symbolic pseudo-differential calculus which…
We introduce anisotropic H\"older spaces useful for the study of the regularity theory for non local kinetic operators $\mathcal{L}$ whose prototypal example is \begin{equation} \mathcal{L} u (t,x,v) = \int_{\mathbb{R}^d} \frac{C_{d,s}}{|v…
We propose a functional framework of fractional Sobolev spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak H\"ormander condition. We characterize these spaces as real interpolation of natural order intrinic…
We prove invariant Harnack inequalities for certain classes of non-divergence form equations of Kolmogorov type. The operators we consider exhibit invariance properties with respect to a homogeneous Lie group structure. The coefficient…
Contractions of Lie algebras are combined with the classical matrix method of Gel'fand to obtain matrix formulae for the Casimir operators of inhomogeneous Lie algebras. The method is presented for the inhomogeneous pseudo-unitary Lie…
The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive…
We consider Kolmogorov-Fokker-Planck operators of the form $$ \mathcal{L}u=\sum_{i,j=1}^{q}a_{ij}(x,t)u_{x_{i}x_{j}}+\sum_{k,j=1}^{N} b_{jk}x_{k}u_{x_{j}}-\partial_{t}u, $$ with $\left( x,t\right) \in\mathbb{R}^{N+1},N\geq q\geq1$. We…
By using commutator methods, we show uniform resolvent estimates and obtain globally smooth operators for self-adjoint injective homogeneous operators $H$ on graded groups, including Rockland operators, sublaplacians and many others. Left…
In this note we announce Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. Applications are given to the…
In this paper we prove Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give applications to a-priori…
On a compact Lie group $G$, we consider the reproducing kernel Hilbert space $\mathcal{H}_K$ associated with the integral kernel $K$ of a left-invariant, positive, symmetric, trace class integral operator on $L^2(G)$. We present lower and…
We present an explicit integration formula for the Haar integral on a compact connected Lie group. This formula relies on a known decomposition of a compact connected simple Lie group into symplectic leaves, when one views the group as a…
A class of generalized nonlinear Kolmogorov equations is investigated. We present the group classification of Lie symmetries of the class with respect to the group of equivalence transformations. We find a number of exact solutions of…
Pseudo $H$-type Lie algebras are a special class of 2-step nilpotent metric Lie algebras, intimately related to Clifford algebras $\Cl_{r,s}$. In this work we propose the classification method for integral orthonormal structures of pseudo…
This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic…
A certain generalization of the algebra $gl(N,{\bf R})$ of first-order differential operators acting on a space of inhomogeneous polynomials in ${\bf R}^{N-1}$ is constructed. The generators of this (non)Lie algebra depend on permutation…
We give a constructive proof of the existence of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov's normalization algorithm to the case of planetary systems, for which…