Nevanlinna representations in several variables

Details Nevanlinna representations in several variables Nevanlinna representations in several variables

2012-03-10

arxiv.org/abs/1203.2261v1

Mathematics

Complex Variables

34 pages

Scientific paper

We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are representation formulae in terms of densely defined self-adjoint operators on a Hilbert space. We introduce three types of structured resolvent of a self-adjoint operator and identify four different types of representation in terms of these resolvents. We relate the types of representation that a function admits to its growth at infinity.

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