Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs

Details Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs

2011-11-25

arxiv.org/abs/1111.5897v1

Constr Approx (2009) 29: 1--21

Computer Science

Information Theory

Scientific paper

Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational splines, the paper presents a reconstruction algorithm of Paley-Wiener functions on graphs from their uniqueness sets.

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