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Nevanlinna Matrices of Entire Functions
Author(s) -
Berg Christian,
Pedersen Henrik L.
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951710104
Subject(s) - mathematics , entire function , polynomial matrix , matrix (chemical analysis) , polynomial , transcendental number , matrix function , pure mathematics , order (exchange) , nevanlinna theory , transcendental function , algebra over a field , matrix polynomial , mathematical analysis , meromorphic function , symmetric matrix , eigenvalues and eigenvectors , materials science , physics , quantum mechanics , finance , economics , composite material
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 arc 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.