scholarly journals Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions

2020 ◽  
Vol 293 (7) ◽  
pp. 1278-1327
Author(s):  
Volodymyr Derkach ◽  
Seppo Hassi ◽  
Mark Malamud
Keyword(s):  
Nevanlinna Functions

Realization of Herglotz–Nevanlinna Functions by Conservative Systems

2015 ◽  
pp. 779-809
Author(s):  
Yury Arlinskiı̆ ◽  
Sergey Belyi ◽  
Eduard Tsekanovskiı̆
Keyword(s):  
Conservative Systems ◽  
Nevanlinna Functions

Convergence of generalized Nevanlinna functions

2011 ◽  
Vol 77 (3-4) ◽  
pp. 425-437
Author(s):  
Heinz Langer ◽  
Annemarie Luger ◽  
Vladimir Matsaev
Keyword(s):  
Nevanlinna Functions

scholarly journals Generalized Schur–Nevanlinna functions and their realizations

2020 ◽  
Vol 92 (5) ◽  
Author(s):  
Lassi Lilleberg
Keyword(s):  
Transfer Functions ◽  
Schur Functions ◽  
Inner Function ◽  
Pontryagin Space ◽  
State Spaces ◽  
Limit Values ◽  
Adjoint Systems ◽  
Generalized Schur Functions ◽  
Nevanlinna Functions ◽  
Weak Similarity

Abstract Pontryagin space operator valued generalized Schur functions and generalized Nevanlinna functions are investigated by using discrete-time systems, or operator colligations, and state space realizations. It is shown that generalized Schur functions have strong radial limit values almost everywhere on the unit circle. These limit values are contractive with respect to the indefinite inner product, which allows one to generalize the notion of an inner function to Pontryagin space operator valued setting. Transfer functions of self-adjoint systems such that their state spaces are Pontryagin spaces, are generalized Nevanlinna functions, and symmetric generalized Schur functions can be realized as transfer functions of self-adjoint systems with Kreĭn spaces as state spaces. A criterion when a symmetric generalized Schur function is also a generalized Nevanlinna function is given. The criterion involves the negative index of the weak similarity mapping between an optimal minimal realization and its dual. In the special case corresponding to the generalization of an inner function, a concrete model for the weak similarity mapping can be obtained by using the canonical realizations.

scholarly journals The Schur Transformation for Generalized Nevanlinna Functions: Interpolation and Self-Adjoint Operator Realizations

2006 ◽  
Vol 1 (2) ◽  
pp. 169-210 ◽  
Author(s):  
Daniel Alpay ◽  
Aad Dijksma ◽  
Heinz Langer ◽  
Yuri Shondin
Keyword(s):  
Adjoint Operator ◽  
Nevanlinna Functions
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