Integral representations of positive definite functions

Abstract

Introduction. During the last decade a school of Russian mathematicians including Krein [l, 2, 3](2), Krein and Krasnoselski [l], Livshitz [l], and Neumark [l] have made contributions to the theory of moments and related problems(3) by the methods of operators in Hubert space. Before this Carleman [l] had used the theory of integral equations to develop the theory and Stone [l] had connected the theory with infinite Jacobi matrices, which method has been elaborated by various other authors.