# Graph Laplacians and discrete reproducing kernel Hilbert spaces from restrictions

Palle Jorgensen, Feng Tian

Abstract:We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding approximate solutions to boundary value problems; using multiresolution-subdivision schemes in continuous domains. In this paper, we turn the tables: our object of study is realistic infinite discrete models in their own right; and we then use an analysis of suitable continuous ...
Applications of the discrete mass property?
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8 months ago
Lester ▴ 15

In the introduction the authors state that there is an associated reversible random walk to the Cameron-Martin and finite energy point models. Then they state that the random walk is transient if and only if finite-energy point-kernels exist. The existence of the finite-energy point-kernels implies that the space has the discrete mass property (i.e. all dirac functions are in the RKHS).

What are the associated random walks in the cases above and are there any other known applications of the discrete mass property?

Reproducing_Kernel_Hilbert_Spaces • 130 views