Entries of indefinite Nevanlinna matrices

In the early 1950's, M. G. Krein characterized the entire functions that are an entry of some Nevanlinna matrix, and the pairs of entire functions that are a row of some Nevanlinna 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 analog of the Nevanlinna matrices plays a role. In the paper, the above-mentioned characterizations are extended to the indefinite situation and the geometry of the associated reproducing kernel Pontryagin spaces is investigated.