Lower order positivity and holomorphic operators

AbstractQuestions concerning holomorphic extensions of operator-valued functions in domains D (or complex manifolds) of Cn are studied. Conditions for such an extension are formulated in terms the of positive-definiteness of order 3 of certain hermitian kernels on D × D. The results of this study constitute a generalization and an extension of previous results of Hindmarsh and FitzGerald and Horn, and recent results of Burbea