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Nevanlinna Matrices of Entire Functions

✍ Scribed by Christian Berg; Henrik L. Pedersen

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 894 KB
Volume: 171
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19951710104

No coin nor oath required. For personal study only.

✦ Synopsis

The notion of a pre-Nevanlinna matrix of entire functions is introduced, and we find necessary and sufficient conditions for an entire function to belong to such a matrix, thereby generalizing previous work of KREIN.

If one of the functions in a pre-Nevanlinna matrix is a polynomial, then the three others are also polynomials and their degrees differ by at most two. If the functions in a pre-Nevanlinna matrix are transcendental they have necessarily the same order, type and indicators.

Actually, in [l] the condition (0.3) is not required for t = co, but it follows from the other conditions by the Theorem of Roucht.

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