Let <¡>(z2) be an even entire function of temperate exponential type, L a selfadjoint realization of -A + c(x), where A is the Laplace-Beltrami operator on a Riemannian manifold, and <¡>(L) the operator given by spectral theory. A PaleyWiener theorem on the support of ( L) is proved, and is used to show that Lu = \u on a suitable domain implies (L)u = <p(\)u, as well as a generalization o...

We consider scattering by general compactly supported semi-classical perturbations of the Euclidean Laplace-Beltrami operator. We show that if the suitably cut-off resolvent of the Hamiltonian quantizes a Lagrangian relation on the product cotangent bundle, the scattering amplitude quantizes the natural scattering relation. In the case when the resolvent is tempered, which is true under some no...

The desymmetrized PSL(2,Z) group is considered. congruence subgroups of the are analysed according to hyperbolic reflections contained. Laplace-Beltrami problem and Hamiltonian associated with operator discussed boundary conditions for grouppal structures. New constructions leaky tori found; in particular, they obtained after generators group, from desymmetrized-triangle ’square-box’ Γ0 subgroup

We develop a unified approach to proving Lp−Lq boundedness of spectral projectors, the resolvent Laplace-Beltrami operator and its derivative on Hd. In case when p q are in duality, dependence implicit constant is shown be sharp. also give partial results question Fourier extension operator. As an application, we prove smoothing estimates for free Schrödinger equation Hd limiting absorption pri...

We propose a framework for the spectral processing of tangential vector fields on surfaces. The basis is a Fourier-type representation of tangential vector fields that associates frequencies with tangential vector fields. To implement the representation for piecewise constant tangential vector fields on triangle meshes, we introduce a discrete Hodge–Laplace operator that fits conceptually to th...

The aim of this paper is to present a new framework for regularization by diffusion. The methods we develop in the sequel can be used to smooth multichannel images, multichannel image sequences (videos), vector fields and orthonormal frame fields in any dimension.1 From a mathematical viewpoint, we deal with vector bundles over Riemannian manifolds and socalled generalized Laplacians. Sections ...

We introduce the generalized helical hypersurface having a space-like axis in five-dimensional Minkowski space. compute first and second fundamental form matrices, Gauss map, shape operator matrix of hypersurface. Additionally, we curvatures by using Cayley–Hamilton theorem. Moreover, give some relations for mean Gauss–Kronecker Finally, obtain Laplace–Beltrami

We provide explicit formulae for the first eigenvalue of Laplace-Beltrami operator on a compact rank one symmetric space (CROSS) endowed with any homogeneous metric. As consequences, we prove that metrics CROSSes are isospectral if and only they isometric, also discuss their stability (or lack thereof) as solutions to Yamabe problem.