Related papers: Hypoelliptic heat kernel on nilpotent Lie groups
In this paper, we study a subelliptic heat kernel on the Lie group SL(2,R) and on its universal covering. The subelliptic structure on SL(2,R) comes from the fibration $SO(2) -> SL(2,R) -> H^2$ and it can be lifted to its universal…
The aim of this paper is to construct (explicit) heat kernels for some hybrid evolution equations which arise in physics, conformal geometry and subelliptic PDEs. Hybrid means that the relevant partial differential operator appears in the…
We suggest a new technique of the asymptotic heat kernel expansion for minimal higher derivative operators of a generic $2M$-th order, $F(\nabla)=(-\Box)^M+\cdots$, in the background field formalism of gauge theories and quantum gravity.…
The aim of this paper is threefold. First, we obtain the precise bounds for the heat kernel on isotropic Heisenberg groups by using well-known results in the three dimensional case. Second, we study the asymptotic estimates at infinity for…
We study the heat kernel transform on a nilmanifold M associated to a H-type group. Using a reduction technique we reduce the problem to the case of Heisenberg groups. The image of $ L^2(M) $ under the heat kernel transform is shown to be a…
In this paper we prove a short time asymptotic expansion of a hypoelliptic heat kernel on an Euclidean space and a compact manifold. We study the "cut locus" case, namely, the case where energy-minimizing paths which join the two points…
In this paper we propose a generalization of the Gilkey-de Witt heat kernel expansion, designed to provide us with a precise estimation of the heat trace of non-negative Schroedinger type differential operators with non-trivial kernel over…
We study heat and wave type equations on a separable Hilbert space $\mathcal{H}$ by considering non-local operators in time with any positive densely defined linear operator with discrete spectrum. We show the explicit representation of the…
Let $\Delta$ be the Laplace--Beltrami operator acting on a non-doubling manifold with two ends $\mathbb R^m \sharp \mathcal R^n$ with $m > n \ge 3$. Let $\frak{h}_t(x,y)$ be the kernels of the semigroup $e^{-t\Delta}$ generated by $\Delta$.…
The lower order terms of the heat kernel expansion at coincident points are computed in the context of finite temperature quantum field theory for flat space-time and in the presence of general gauge and scalar fields which may be non…
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The…
Based on the theory of Dunkl operators, this paper presents a general concept of multivariable Hermite polynomials and Hermite functions which are associated with finite reflection groups on $\b R^N$. The definition and properties of these…
We develop a new heat kernel method that is suited for a systematic study of the renormalization group flow in Horava gravity (and in Lifshitz field theories in general). This method maintains covariance at all stages of the calculation,…
We study the subelliptic heat kernels of the CR three dimensional solvable Lie groups. We first classify all left-invariant sub-Riemannian structures on three dimensional solvable Lie groups and obtain representations of these groups. We…
We study the index of the $G$-invariant elliptic pseudo-differential operator acting on a complete Riemannian manifold, where a unimodular, locally compact group $G$ acts properly and cocompactly. An $L^2$-index formula was obtained using…
The short-time heat kernel expansion of elliptic operators provides a link between local and global features of classical geometries. For many geometric structures related to (non-)involutive distributions, the natural differential…
In this note, we look at some hypoelliptic operators arising from nilpotent rank 2 Lie algebras. In particular, we concentrate on the diffusion generated by three Brownian motions and their three L\'evy areas, which is the simplest…
We give sharp asymptotic estimates at infinity of all radial partial derivatives of the heat kernel on H-type groups. As an application, we give a new proof of the discreteness of the spectrum of some natural sub-Riemannian…
In this paper, we begin a quantization program for nilpotent orbits of a real semisimple Lie group. These orbits and their covers generalize the symplectic vector space. A complex structure polarizing the orbit and invariant under a maximal…
We construct an index of first-order, self-adjoint, elliptic differential operators in the $K$-theory of a Fr\'echet algebra of smooth kernels with faster than exponential off-diagonal decay. We show that this index can be represented by an…