Related papers: The Standard Laplace Operator
Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete…
We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…
This paper presents a generalisation of Sylvester's law of inertia to real non-degenerate quadratic forms on a fixed real vector bundle over a connected locally connected paracompact Hausdorff space. By interpreting the classical inertia as…
On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides…
The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and…
In this paper, an explicit expression is obtained for the conformally invariant higher spin Laplace operator $\mathcal{D}_{\lambda}$, which acts on functions taking values in an arbitrary (finite-dimensional) irreducible representation for…
Consider a fractional operator $P^s$, $0<s<1$, for connection Laplacian $P:=\nabla^*\nabla+A$ on a smooth Hermitian vector bundle over a closed, connected Riemannian manifold of dimension $n\geq 2$. We show that local knowledge of the…
Recently a new technique in the harmonic analysis on symmetric spaces was suggested based on certain remarkable representations of affine and double affine Hecke algebras in terms of Dunkl and Demazure operators instead of Lie groups and…
A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the…
We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal…
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…
Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of…
Using the embedded gradient vector field method (see P. Birtea, D. Comanescu, Hessian operators on constraint manifolds, J. Nonlinear Science 25, 2015), we present a general formula for the Laplace-Beltrami operator defined on a constraint…
The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$ on a Hilbert…
This note is an attempt to extend "Geometric Langlands Conjecture" from algebraic curves to algebraic surfaces. We introduce certain Hecke-type operators on vector bundles on an algebraic surface. The crucial observation is that the algebra…
If M is a smooth compact oriented Riemannian manifold of dimension n=4k+2, with or without boundary, and F is a vector bundle on M with an inner product and a flat connection, we construct a modification of the Hodge star operator on the…
The Lagrangian mechanical consideration of the dynamics of ideal incompressible hydrodynamic, magnetohydrodynamic, and Hall magnetohydrodynamic media, which are formulated as dynamical systems in appropriate Lie groups equipped with…
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…
In order to account for all possible contractions allowed by the presence of the solder form, a generalized Hodge dual is defined for the case of soldered bundles. Although for curvature the generalized dual coincides with the usual one,…
We explore the existence of a class of generalised Laplace maps for third order partial differential operators of the form…