On infinitely divisible matrices, kernels, and functions

SummaryGeneralizations and applications of a recent theorem of C. Loewner on nonnegative quadratic forms have led to interesting new results and to some especially simple derivations of well-known theorems from a unified point of view. In this note we discuss two applications to the study of characteristic functions and completely monotonic functions, and show how the classical representation theorems for infinitely divisible laws may be obtained.