منابع مشابه
Survey of Spectra of Laplacians on Finite Symmetric Spaces
Some of the research surveyed here was supported by the Mathematical Sciences Research Institute in Berkeley, CA. Research at MSRI is supported in part by NSF grant DMS-9022140. We survey what is known about spectra of combinatorial Laplacians (or adjacency operators) of graphs on the simplest finite symmetric spaces. This work is joint with J. Angel, N. Celniker, A. Medrano, P. Myers, S. Poulo...
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The Laplacian of an undirected graph is a square matrix, whose eigenvalues yield important information. We can regard graphs as one-dimensional simplicial complexes, and as whether there is a generalisation of the Laplacian operator to simplicial complexes. It turns out that there is, and that is useful for calculating real Betti numbers [8]. Duval and Reiner [5] have studied Laplacians of a sp...
متن کاملLaplacians on lattices
We consider some lattices and look at discrete Laplacians on these lattices. In particular, we look at solutions of the equation △(1)φ = △(2)Z, where △(1) and △(2) denote two such Laplacians on the same lattice. We show that, in one dimension, when △(i) i = 1, 2 denote △(1)φ = φ(i+ 1)− φ(i− 1)− 2φ(i) and △(2)Z = Z(i+ 2)− Z(i− 2)− 2Z(i) this equation has a simple solution φ(i) = Z(i+ 1) + Z(i− 1...
متن کاملHodge Laplacians on graphs
This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian. We will discuss basic properties including cohomology and Hodge theory. At the end we will also discuss the nonlinear Laplacian on a graph, a nonlinear generalization of the graph Laplacian as its name implies. These generalized Laplacians will be constructed out of coboun...
متن کاملMEAN VALUE INTERPOLATION ON SPHERES
In this paper we consider multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have concentric spheres. Indeed, we consider the problem in three variables when it is not correct.
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2019
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2019.12.855