For the interpolation of graph signals with generalized shifts a basis function (GBF), we introduce concept positive definite functions on graphs. This merges kernel-based spectral theory graphs and can be regarded as analog radial in Euclidean spaces or spherical functions. We provide several descriptions graphs, most relevant one is Bochner-type characterization terms Fourier coefficients. Th...

In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on L positive definite functions to matrix valued L positive definite functions. We show that a matrix-valued continuous L positive definite function can always be written as a convolution of a L positive definite function with itself. We also prove that, give...