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Some remarks on Nevanlinna’s theory in a Hilbert space. (English) Zbl 0920.30022
H. J. W. Ziegler [Vector-valued Nevanlinna Theory (1982; Zbl 0496.30026)] generalized the Poisson-Jensen-Nevanlinna formula for meromorphic functions so as to extend classical Nevanlinna theory to finite dimensional vector-valued meromorphic functions. In the paper under review the authors note that some of Ziegler’s ideas can be adapted so as to establish Nevanlinna theory in an infinite dimensional subspace of each infinite dimensional Hilbert space.
MSC:
30D35Distribution of values (one complex variable); Nevanlinna theory