We prove the analytic continuation of the resolvent of the Laplacian on asymptotically hyperbolic spaces on differential forms, including high energy estimates in strips. This is achieved by placing the spectral family of the Laplacian within the framework developed, and applied to scalar problems, by the author recently, roughly by extending the problem across the boundary of the compactificat...

Digital Geometry Processing (DGP) is concerned with the construction of signal processing style algorithms that operate on surface geometry, typically specified by an unstructured triangle mesh. An active subfield of study involves the utilization of discrete mesh Laplacian operators for eigenvalue decomposition, mimicking the effect of discrete Fourier analysis on mesh geometry. In this paper,...

We introduce a one-parameter family of massive Laplacian operators (∆)k∈[0,1) defined on isoradial graphs, involving elliptic functions. We prove an explicit formula for minus the inverse of ∆, the massive Green function, which has the remarkable property of only depending on the local geometry of the graph, and compute its asymptotics. We study the corresponding statistical mechanics model of ...

Bony and Häfner have recently obtained positive commutator estimates on the Laplacian in the low-energy limit on asymptotically Euclidean spaces; these estimates can be used to prove local energy decay estimates if the metric is non-trapping. We simplify the proof of the estimates of Bony-Häfner and generalize them to the setting of scattering manifolds (i.e. manifolds with large conic ends), b...

In Gauss-Bonnet braneworld cosmology, the Friedmann equation of our four-dimensional universe on 3-brane is modified in a high energy regime (Gauss-Bonnet regime), while the standard expansion law is reproduced in low energies (standard regime). We investigate the Gauss-Bonnet braneworld cosmological effect on the thermal relic density of cold dark matter when the freeze-out of the dark matter ...

In this paper we give a simple characterization of the Laplacian spectra of a family of graphs as the eigenvalues of symmetric tridiagonal matrices. In addition, we apply our result to obtain an upper and lower bounds for the Laplacian-energy-like invariant of these graphs. The class of graphs considered are obtained by copies of modified generalized Bethe trees (obtained by joining the vertice...

We study the low energy asymptotics of periodic and random Laplace operators on Cayley graphs of amenable, finitely generated groups. For the periodic operator the asymptotics is characterised by the van Hove exponent or zeroth Novikov-Shubin invariant. The random model we consider is given in terms of an adjacency Laplacian on site or edge percolation subgraphs of the Cayley graph. The asympto...

In this paper, a Gauss–Seidel method with oblique direction (GSO) is proposed for finding the least-squares solution to system of linear equations, where coefficient matrix may be full rank or deficient and overdetermined underdetermined. Through method, number iteration steps running time can reduced greater extent find solution, especially when columns A are close correlation. It theoreticall...