Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

1997 ◽  
Author(s):  
Daniel Alpay ◽  
Aad Dijksma ◽  
James Rovnyak ◽  
Hendrik de Snoo
Keyword(s):  
Reproducing Kernel ◽  
Schur Functions ◽  
Pontryagin Spaces

Realization and Factorization in Reproducing Kernel Pontryagin Spaces

2001 ◽  
pp. 43-65
Author(s):  
D. Alpay ◽  
A. Dijksma ◽  
J. Rovnyak ◽  
H. S. V. de Snoo
Keyword(s):  
Reproducing Kernel ◽  
Pontryagin Spaces

scholarly journals On Some Operator Colligations and Associated Reproducing Kernel Pontryagin Spaces

1996 ◽  
Vol 136 (1) ◽  
pp. 39-80 ◽  
Author(s):  
D. Alpay ◽  
V. Bolotnikov ◽  
A. Dijksma ◽  
H. de Snoo
Keyword(s):  
Reproducing Kernel ◽  
Pontryagin Spaces

scholarly journals Reproducing kernel almost Pontryagin spaces

2014 ◽  
Vol 461 ◽  
pp. 271-317 ◽  
Author(s):  
Harald Woracek
Keyword(s):  
Reproducing Kernel ◽  
Pontryagin Spaces

scholarly journals Unitary Boundary Pairs for Isometric Operators in Pontryagin Spaces and Generalized Coresolvents

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
D. Baidiuk ◽  
V. Derkach ◽  
S. Hassi
Keyword(s):  
Hilbert Space ◽  
Schur Functions ◽  
Characteristic Functions ◽  
General Notion ◽  
Pontryagin Space ◽  
Isometric Operator ◽  
Pontryagin Spaces ◽  
Alternative Approach ◽  
Boundary Triple ◽  
Space Case

AbstractAn isometric operator V in a Pontryagin space $${{{\mathfrak {H}}}}$$ H is called standard, if its domain and the range are nondegenerate subspaces in $${{{\mathfrak {H}}}}$$ H . A description of coresolvents for standard isometric operators is known and basic underlying concepts that appear in the literature are unitary colligations and characteristic functions. In the present paper generalized coresolvents of non-standard Pontryagin space isometric operators are described. The methods used in this paper rely on a new general notion of boundary pairs introduced for isometric operators in a Pontryagin space setting. Even in the Hilbert space case this notion generalizes the earlier concept of boundary triples for isometric operators and offers an alternative approach to study operator valued Schur functions without any additional invertibility requirements appearing in the ordinary boundary triple approach.

Reproducing Kernel Quaternionic Pontryagin Spaces

2004 ◽  
Vol 50 (4) ◽  
pp. 431-476 ◽  
Author(s):  
Daniel Alpay ◽  
Michael Shapiro
Keyword(s):  
Reproducing Kernel ◽  
Pontryagin Spaces

Construction of cubature formulas with fourth and fifth degrees by the reproducing kernel and Radon methods

2020 ◽  
Vol 2020 (2) ◽  
pp. 76-84
Author(s):  
G.P. Ismatullaev ◽  
S.A. Bakhromov ◽  
R. Mirzakabilov
Keyword(s):  
Reproducing Kernel ◽  
Cubature Formulas
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