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...

A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...