Von Neumann indices and classes of positive definite functions (Q2924906)

As the authors state, the paper presents a correspondence between two problems: (i) the problem of finding continuous positive definite extensions of functions which are defined on open bounded domains \(\Omega\) in \(R\), on the one hand; and (ii) spectral theory for elliptic differential operators acting on \(\Omega\) (constant coefficients). A series of results, concerning positive definite continuous functions defined locally and reproducing-kernel Hilbert spaces, are given.