Then the spectrum for the Laplace Beltrami operator on is discrete and real, since the Laplace operator is self adjoint with compact resolvent; that is
22.
As many people guessed, this article just gives a badly explained description of the spectrum of the Laplace operator with Dirichlet and Neumann boundary conditions.
23.
The right-hand side is the radial term of the Laplace operator, so this differential equation is a special case of the Poisson equation.
24.
In mathematics, the "'Ornstein Uhlenbeck operator "'is a generalization of the Laplace operator to an infinite-dimensional setting.
25.
The discrete Laplace operator occurs in physics problems such as the Ising model and loop quantum gravity, as well as in the study of discrete dynamical systems.
26.
The differential equation containing the Laplace operator is then transformed into a variational formulation, and a system of equations is constructed ( linear or eigenvalue problems ).
27.
All "'self-adjoint matching conditions "'of the Laplace operator on a graph can be classified according to a scheme of Kostrykin and Schrader.
28.
For the case of a finite-dimensional graph ( having a finite number of edges and vertices ), the discrete Laplace operator is more commonly called the Laplacian matrix.
29.
Another generalization of the Laplace operator that is available on pseudo-Riemannian manifolds uses the exterior derivative, in terms of which the geometer's Laplacian " is expressed as
30.
In mathematics, the "'discrete Laplace operator "'is an analog of the continuous Laplace operator, defined so that it has meaning on a discrete grid.
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