Schur-class multipliers on the Arveson space: De Branges-Rovnyak reproducing kernel spaces and commutative transfer-function realizations

Journal of Mathematical Analysis and Applications

Volumn 341, Issue 1, 2008, Pages 519-539

  Ball, Joseph A ^a   Bolotnikov, Vladimir ^b   Fang, Quanlei ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b Dept of Economics and Thomas Jefferson Program in Public Policy at the College of William and Mary   (United States)

Author keywords

Inner multipliers; Operator valued functions; Schur class multipliers

Indexed keywords

EID: 38749096262     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.10.033     Document Type: Article

References (29)

1. Agler J., and McCarthy J.E. Complete Nevanlinna-Pick kernels. J. Funct. Anal. 175 1 (2000) 111-124
2. Alpay D., and Kaptanoǧlu H. Some finite-dimensional backward shift-invariant subspaces in the ball and a related interpolation problem. Integral Equations Operator Theory 42 1 (2002) 1-21
3. Aronszajn N. Theory of reproducing kernels. Trans. Amer. Math. Soc. 68 (1950) 337-404
4. *-algebras. III. Multivariable operator theory. Acta Math. 181 2 (1998) 159-228
5. d]. J. Reine Angew. Math. 522 (2000) 173-236
6. J.A. Ball, V. Bolotnikov, Q. Fang, Multivariable backward-shift invariant subspaces and observability operators, Multidimensional Syst. Signal Process., in press
7. Ball J.A., Bolotnikov V., and Fang Q. Transfer-function realization for multipliers of the Arveson space. J. Math. Anal. Appl. 333 1 (2007) 68-92
8. J.A. Ball, V. Bolotnikov, Q. Fang, Schur-class multipliers on the Fock space: De Branges-Rovnyak reproducing kernel spaces and transfer-function realizations, in: Teberiu Constantinescu Memorial Volume, Theta, Bucharest, in press
9. Ball J.A., Gohberg I., and Rodman L. Interpolation of Rational Matrix Functions. Oper. Theory Adv. Appl. vol. 45 (1990), Birkhäuser, Basel
10. Ball J.A., and Raney M. Discrete-time dichotomous well-posed linear systems and generalized Schur-Nevanlinna-Pick interpolation. Complex Anal. Operator Theory 1 1 (2007) 1-54
11. Ball J.A., Trent T.T., and Vinnikov V. Interpolation and commutant lifting for multipliers on reproducing kernels Hilbert spaces. In: Bart H., Gohberg I., and Ran A.C.M. (Eds). Operator Theory and Analysis. Oper. Theory Adv. Appl. vol. 122 (2001), Birkhäuser, Basel 89-138
12. Ball J.A., and Vinnikov V. Lax-Phillips scattering and conservative linear systems: A Cuntz-algebra multidimensional setting. Mem. Amer. Math. Soc. 178 837 (2005) 1-101
13. Beurling A. On two problems concerning linear transformations in Hilbert space. Acta Math. 81 (1949) 239-255
14. Bhattacharyya T., Eschmeier J., and Sarkar J. Characteristic function of a pure commuting contractive tuple. Integral Equations Operator Theory 53 1 (2005) 23-32
15. Bhattacharyya T., Eschmeier J., and Sarkar J. On c.n.c. commuting contractive tuples. Proc. Indian Acad. Sci. Math. Sci. 116 3 (2006) 299-316
16. Bhattacharyya T., and Sarkar J. Characteristic function for polynomially contractive commuting tuples. J. Math. Anal. Appl. 321 1 (2006) 242-259
17. de Branges L., and Rovnyak J. Canonical models in quantum scattering theory. In: Wilcox C. (Ed). Perturbation Theory and Its Applications in Quantum Mechanics (1966), Holt, Rinehart and Winston, New York 295-392
18. de Branges L., and Rovnyak J. Square Summable Power Series (1966), Holt, Rinehart and Winston, New York
19. Gleason A.M. Finitely generated ideals in Banach algebras. J. Math. Mech. 13 (1964) 125-132
20. Greene D.C., Richter S., and Sundberg C. The structure of inner multipliers on spaces with complete Nevanlinna-Pick kernels. J. Funct. Anal. 194 2 (2002) 311-331
21. Halmos P.R. Shifts on Hilbert spaces. J. Reine Angew. Math. 208 (1961) 102-112
22. Lax P.D. Translation invariant spaces. Acta Math. 101 (1959) 163-178
23. McCullough S., and Trent T.T. Invariant subspaces and Nevanlinna-Pick kernels. J. Funct. Anal. 178 1 (2000) 226-249
24. Sz.-Nagy B., and Foias C. Harmonic Analysis of Operators on Hilbert Space (1970), North-Holland, Amsterdam
25. Popescu G. Multi-analytic operators and some factorization theorems. Indiana Univ. Math. J. 38 3 (1989) 693-710
26. Popescu G. Characteristic functions for infinite sequences of noncommuting operators. J. Operator Theory 22 1 (1989) 51-71
27. Popescu G. Operator theory on noncommutative varieties. Indiana Univ. Math. J. 55 2 (2006) 389-442
28. Popescu G. Operator theory on noncommutative varieties II. Proc. Amer. Math. Soc. 135 7 (2007) 2151-2164
29. n (1980), Springer-Verlag, Berlin