Related papers: Laplace operators and diffusions in tangent bundle…
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on forms and associated semigroups are considered. Their probabilistic interpretation…
We consider odd Laplace operators acting on densities of various weight on an odd Poisson (= Schouten) manifold $M$. We prove that the case of densities of weight 1/2 (half-densities) is distinguished by the existence of a unique odd…
The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator…
We derive explicit restriction and continuation formulas between n-dimensional (Anti)-de Sitter spaces and the (n + 1)-dimensional Minkowskian ambient space for the codifferential and Laplace-de Rham operators acting on p-forms.
The aim of the paper is to study some dynamic aspects coming from a tangent form, i.e. a time dependent differential form on a tangent bundle. The action on curves of a tangent form is natural associated with that of a second order…
We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on $T^*M$ is made into a space of (full) symbols of operators acting on forms on $M$. This gives rise to the composition of symbols,…
We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum…
In this paper, we study the boundedness of a class of fractional integrals and derivatives associated with Laguerre polynomial expansions on Laguerre Lipschitz spaces. The consideration of such operators is motivated by the study of…
In this study, Hamiltonian and Lagrangian theories, which are mathematical models of mechanical systems, are structured on the horizontal and the vertical distributions of tangent and cotangent bundles. In the end, the geometrical and…
We introduce a new class of pseudodifferential operators, called Heisenberg semiclassical pseudodifferential operators, to study the space of sections of a power of a line bundle on a compact manifold, in the limit where the power is large.…
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
This paper is concerned with the Poisson transform of differential forms on the hyperbolic space $H^n(\mathbb R)$. Consider an integer $p$ such that $1\leqslant p\leqslant n$ and let $q$ be either $p-1$ or $p$. For $1<r<\infty$, we prove…
This paper outlines a method where a brachistochrone is developed for the hyperbolic plane. This technique is then used to calculate the Fubini-Study metric and consequent Laplacian operator. We discuss the various systems of eigenfunctions…
Classical settings of discrete and continuous orthogonal expansions, like Laguerre, Bessel and Jacobi, are associated with second order differential operators playing the role of the Laplacian. These depend on certain parameters of type…
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
The purpose of this work is to study Lie superalgebroid structures on the space of superdifferential $1$-forms over the supermanifolds whose superfunctions are the differential forms on its underlying manifold. These superalgbroids are…
Using the notion of commutative operator vessels, this work investigates de Branges-Rovnyak spaces whose elements are sections of a line bundle of multiplicative half-order differentials on a compact real Riemann surface. As a special case,…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
Laplacians associated with domains with singular boundary conditions and are considered together with semigroups on generalized Sobolev spaces, they generate. Applications are given to stochastic PDEs with singular boundary conditions.