Entries of indefinite Nevanlinna matrices

Abstract

In the early 1950’s M.G.Krein characterised those entire functions which are an entry of some Nevanlinna matrix, and those pairs of entire functions which are a row of some such matrix. In connection with Pontryagin space versions of Krein’s theory of entire operators and de Branges’ theory of Hilbert spaces of entire functions, an indefinite analogue of Nevanlinna matrices plays a role. In this paper we extend the mentioned characterisations to the indefinite situation and investigate the geometry of associated reproducing kernel Pontryagin spaces. AMS MSC 2010: 46C20, 34B20, 30D10, 30D15