Infinitely Divisible Matrices, Kernels, and Functions |
Common terms and phrases
C₁ choice of arguments completely monotonic function completely monotonic sequence consistent choice continuous function continuous kernel Conversely Corollary define divisible characteristic function divisible completely monotonic divisible positive definite du(e du(t du(x dv(t dµ(t dµ(x equivalent finite function f(z graph Green's function Hermitian Hilbert space implies incidence matrix inequality infinitely divisible characteristic infinitely divisible completely infinitely divisible kernels infinitely divisible positive integer interpolation problem irreducible component kernel K(x,y Lemma Let K(P,Q Let K(x,y Loewner log x-y M₂ monotonic function nodes nonnegative measure nonnegative quadratic form nx n matrix Pick's theorem principally infinitely divisible probability measure Proof quadratic form real valued representation formula Schur product theorem semigroup symmetric matrix teristic function Theorem 2.2 three point property unique unit disc univalent analytic function zeros αμ