Hankel matrices, positive functions and related questions Original Research Article

This paper is concerned with the subclass of positive functions that can be associated to nonnegative definite Hankel matrices and with its extension to the subclass of appropriate pseudo-positive functions of finite index so as to accommodate the indefinite case. Although the treatment is largely inspired by the somewhat overlooked work of Akhiezer in the context of Nevanlinna functions, it aims at presenting a modern account of the results available in the field as well as of their generalization beyond the mathematical limits of the original derivation. The Hankel matrix extension problem is discussed and solved in a simple manner as an illustration of the proposed techniques.