Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

A UNITARY LINEAR SYSTEM ON THE BIDISK

  • Yang, Meehyea (Department of Mathematics, University of Incheon) ;
  • Hong, Bum-Il (Department of Mathematics, Kyung Hee University)
  • Received : 2007.06.18
  • Published : 2007.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

Let S($z_1$, $z_2$) be a power series with operator coefficients such that multiplication by 5($z_1$, $z_2$) is a contractive transformation in the Hilbert space $\mathbf{H}_2$($\mathbb{D}^2$, C). In this paper we show that there exists a Hilbert space D($\mathbb{D}$,$\bar{S}$) which is the state space of extended canonical linear system with a transfer fucntion $\bar{S}$(z).

Keywords

References

  1. D. Alpay, V. Bolotnikov, A. Dijksma and C. Sadosky, Hilbert spaces contractively included in the Hardy space of the Bidisk, Positivity 5 (2001), 25-50. https://doi.org/10.1023/A:1009826406222
  2. D. Alpay, A. Dijksma and J. Rovnyak, A theorem of Beurling-Lax type for Hilbert spaces of functions analytic in the unit ball, Integral Equations and Operator Theory 47 (2003), 251-274. https://doi.org/10.1007/s00020-002-1161-4
  3. D. Alpay, A. Dijksma, J. Rovnyak and H, de Snoo, Schur functions, operator colligations and reproducing kernel Pontryagin spaces, Operator Theory: Advances and Applications 96 (1997), Birkhauser Verlag, Basel.
  4. V. Bolotnikov, Interpolation for multipliers on reproducing kernel Hilbert spaces, Proc. Amer. Math. Soc. 131 (2002), 1373-1383.
  5. L. de Branges, Krein spaces of analytical functions, J. Functional Analysis 81 (1988), 219-259. https://doi.org/10.1016/0022-1236(88)90099-7
  6. L. de Branges, Complementation in Krein spaces, Trans. Amer. Math. Soc. 305 (1988), 277-291.
  7. L. de Branges, Factorization in Krein spaces, J. Functional Analysis 124 (1994), 228-262. https://doi.org/10.1006/jfan.1994.1107
  8. L. de Branges and J. Rovnyak, Canonical models in quantum scattering theory, Perturbation Theory and its Applications in Quantum Mechanics, Wiley, New York, 1966.
  9. M. Yang, A construction of unitary linear systems, Integral Equations and Operator Theory 19 (1994), 477-499. https://doi.org/10.1007/BF01299845
  10. M. Yang, Reproducing Kernel Krein spaces, J. Appl. Math. & Computing 8 (2001), 659-668.

Cited by

  1. FACTORIZATION OF A HILBERT SPACE ON THE BIDISK vol.31, pp.4, 2009, https://doi.org/10.5831/HMJ.2009.31.4.479