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On Representations of Matrix Valued Nevanlinna Functions by u ‐ Resolvents
Author(s) -
Kaltenbäck Michael,
Woracek Harald
Publication year - 1999
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.3212050106
Subject(s) - mathematics , resolvent , pontryagin's minimum principle , scalar (mathematics) , pure mathematics , matrix function , matrix (chemical analysis) , mathematical analysis , eigenvalues and eigenvectors , optimal control , symmetric matrix , mathematical optimization , physics , geometry , materials science , quantum mechanics , composite material
We show that every matrix valued generalized Nevanlinna function can be represented as a u ‐resolvent of a certain selfadjoint relation acting in a Pontryagin space. The negative index of this Pontryagin space may be larger than the number of negative squares of the given function. The minimal index of negative squares which is needed to obtain such a representation is determined. In the case of scalar functions, the results presented give rise to some new classes of generalized Nevanlinna functions.