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For the interpolation of graph signals with generalized shifts of a graphbasis function (GBF), we introduce the concept of positive definite functionson graphs. This concept merges kernel-based interpolation with spectral theoryon graphs and can be regarded as a graph analog of radial basis functioninterpolation in euclidean spaces or spherical basis functions. We provideseveral descriptions of positive definite functions on graphs, the mostrelevant one is a Bochner-type characterization in terms of positive Fouriercoefficients. These descriptions allow us to design GBF's and to study GBFinterpolation in more detail: we are able to characterize the native spaces ofthe interpolants, we provide explicit estimates for the interpolation error andobtain bounds for the numerical stability. As a final application, we show howGBF interpolation can be used to get quadrature formulas on graphs.

Graph signal interpolation with Positive Definite Graph Basis Functions