Graph Laplacians and discrete reproducing kernel Hilbert spaces from restrictions

Palle Jorgensen; Feng Tian

Graph Laplacians and discrete reproducing kernel Hilbert spaces from restrictions

Functional Analysis 2015-08-17 v2

Authors: 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 counterpart problems, but now serving as a tool for obtaining solutions in the discrete world.

Keywords

reproducing kernel hilbert space hilbert functions operator theory on hilbert spaces

Cite

@article{arxiv.1501.04954,
  title  = {Graph Laplacians and discrete reproducing kernel Hilbert spaces from restrictions},
  author = {Palle Jorgensen and Feng Tian},
  journal= {arXiv preprint arXiv:1501.04954},
  year   = {2015}
}

Comments

26 pages, 6 figures. arXiv admin note: text overlap with arXiv:1501.02310

Graph Laplacians and discrete reproducing kernel Hilbert spaces from restrictions

Abstract

Keywords

Cite

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