Realization and Factorization in Reproducing Kernel Pontryagin Spaces

Author(s):  
D. Alpay ◽  
A. Dijksma ◽  
J. Rovnyak ◽  
H. S. V. de Snoo
1996 ◽  
Vol 136 (1) ◽  
pp. 39-80 ◽  
Author(s):  
D. Alpay ◽  
V. Bolotnikov ◽  
A. Dijksma ◽  
H. de Snoo

Author(s):  
Daniel Alpay ◽  
Aad Dijksma ◽  
James Rovnyak ◽  
Hendrik de Snoo

2014 ◽  
Vol 461 ◽  
pp. 271-317 ◽  
Author(s):  
Harald Woracek

2004 ◽  
Vol 50 (4) ◽  
pp. 431-476 ◽  
Author(s):  
Daniel Alpay ◽  
Michael Shapiro

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

Author(s):  
Michael T Jury ◽  
Robert T W Martin

Abstract We extend the Lebesgue decomposition of positive measures with respect to Lebesgue measure on the complex unit circle to the non-commutative (NC) multi-variable setting of (positive) NC measures. These are positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz $C^{\ast }-$algebra, the $C^{\ast }-$algebra of the left creation operators on the full Fock space. This theory is fundamentally connected to the representation theory of the Cuntz and Cuntz–Toeplitz $C^{\ast }-$algebras; any *−representation of the Cuntz–Toeplitz $C^{\ast }-$algebra is obtained (up to unitary equivalence), by applying a Gelfand–Naimark–Segal construction to a positive NC measure. Our approach combines the theory of Lebesgue decomposition of sesquilinear forms in Hilbert space, Lebesgue decomposition of row isometries, free semigroup algebra theory, NC reproducing kernel Hilbert space theory, and NC Hardy space theory.


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