Reproducing Kernel Quaternionic Pontryagin Spaces

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

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

scholarly journals Reproducing kernel almost Pontryagin spaces

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

scholarly journals Lebesgue Decomposition of Non-Commutative Measures

2020 ◽  
Author(s):  
Michael T Jury ◽  
Robert T W Martin
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Fock Space ◽  
Reproducing Kernel Hilbert Space ◽  
Semigroup Algebra ◽  
Space Theory ◽  
Lebesgue Decomposition ◽  
Sesquilinear Forms ◽  
Positive Linear Functionals ◽  
Algebra Theory

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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