A bitangential interpolation problem on the closed unit ball for multipliers of the Arveson space

Integral Equations and Operator Theory

Volumn 46, Issue 2, 2003, Pages 125-164

  Ball, Joseph A ^a   Bolotnikov, Vladimir ^b  

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

^b William and Mary   (United States)

Author keywords

Arveson space; Multipliers; Unitary extensions

Indexed keywords

EID: 0037900822     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000200300022     Document Type: Article

References (41)

1. M. Abate, Angular derivatives in strongly pseudoconvex domains, Proc. Sympos. Pure Math., 52 (1991), 23-40.
2. J. Agler and J. E. McCarthy, Complete Nevanlinna-Pick kernels, J. Funct. Anal., 175 (2000), 111-124.
3. N. Akhiezer and M.G. Kreǐn, Some questions in the theory of moments, Article II, Translations of Mathematical Monographs, Amer. Math. Soc., 1962.
4. D. Alpay, V. Bolotnikov and T. Kaptanoǧlu, The Schur algorithm and reproducing kernel Hilbert spaces in the ball, Linear Algebra Appl. 342 (2002), 163-186.
5. D. Alpay and C. Dubi, Boundary interpolation in the ball, in Linear Algebra Appl., to appear.
6. A. Arias and G. Popescu, Noncommutative interpolation and Poisson transforms, Israel J. Math. 115 (2000), 205-234.
7. N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), 337-404.
8. D.Z. Arov and L.Z. Grossman, Scattering matrices in the theory of unitary extensions of isometric operators, Soviet Math. Dokl., 270 (1983), 17-20.
9. D.Z. Arov and L.Z. Grossman, Scattering matrices in the theory of unitary extensions of isometric operators, Math. Nachr., 157 (1992), 105-123.
10. W. Arveson, Subalgebras of C*-algebras. III. Multivariable operator theory, Acta Math. 181 (1998), no. 2, 159-228.
11. J.A. Ball, Interpolation problems of Pick-Nevanlinna and Loewner type for meromorphic matrix functions, Integral Equations and Operator Theory, 6 (1983), 804-840.
12. J. A. Ball and V. Bolotnikov, On a bitangential interpolation problem for contractive valued functions on the unit ball, Linear Algebra Appl., to appear.
13. J.A. Ball, I. Gohberg and L. Rodman, Interpolation of Rational Matrix Functions, Birkhäuser Verlag, Basel, 1990.
14. J.A. Ball, I. Gohberg and L. Rodman, Boundary Nevanlinna-Pick interpolation for rational matrix functions, J. Math. Systems, Estimation, and Control 1 (1991), 131-164.
15. J.A. Ball and J.W. Helton, Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix-functions: parametriztion of the set of all solutions, Integral Equations and Operator Theory 9 (1986), 155-203.
16. J. A. Ball, T. T. Trent and V. Vinnikov, Interpolation and commutant lifting for multipliers on reproducing kernels Hilbert spaces, in: Operator Theory and Analysis: The M.A. Kaashoek Anniversary Volume (Workshop in Amsterdam, Nov. 1997), pages 89-138, OT 122, Birkhauser-Verlag, Basel-Boston-Berlin, 2001.
17. V. Bolotnikov, A boundary Nevanlinna-Pick problem for a class of analytic matrix-valued functions in the unit ball, Linear Algebra Appl., to appear.
18. V. Bolotnikov and H. Dym, On degenerate interpolation, entropy and extremal problems for matrix Schur functions, Integral Equations Operator Theory, 32 (1998), No. 4, 367-435.
19. V. Bolotnikov and H. Dym, On boundary interpolation for matrix Schur functions, Preprint MCS99-22, Department of Mathematics, The Weizmann Institute of Science, Israel.
20. C.I. Byrnes, S.V. Gusev and A. Lindquist, From finite covariance windows to modeling filters: a convex optimization approach, SIAM Review 43(4) (2001), 645-675.
21. C. Carathéodory, Über die Winkelderivierten von beschränkten analytischen Funktionen, Sitzungber. Preuss. Akad. Wiss. 4 (1929), 1-18.
22. K. R. Davidson and D. R. Pitts, Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras, Integral Equations Operator Theory 31 (1998), no. 3, 321-337.
23. H. Dym, J contractive matrix functions, reproducing kernel spaces and interpolation, CBMS Lecture Notes, vol. 71, Amer. Math. Soc., Rhodes Island, 1989.
24. G. Julia, Extension nouvelle d'un lemme de Schwarz, Acta Math. 42 (1920), 349-355.
25. V. Katsnelson, A. Kheifets, and P. Yuditskii. An abstract interpolation problem and the extension theory of isometric operators, in: Topics in Interpolation Theory (Ed. H. Dym, B. Fritzsche, V. Katsnelson, and B. Kirstein), Operator Theory: Advances and Applications OT 95, pages 283-297. Birkhäuser Verlag, Basel, 1997. Translated from: Operators in function spaces and problems in function theory, pp. 83-96 (Naukova-Dumka, Kiev, 1987. Edited by V.A. Marchenko).
26. V. Katsnelson, A. Kheifets, and P. Yuditskii. An abstract interpolation problem and the extension theory of isometric operators, in: Topics in Interpolation Theory (Ed. H. Dym, B. Fritzsche, V. Katsnelson, and B. Kirstein), Operator Theory: Advances and Applications OT 95, pages 283-297. Birkhäuser Verlag, Basel, 1997. Translated from: Operators in function spaces and problems in function theory, pp. 83-96 (Naukova-Dumka, Kiev, 1987. Edited by V.A. Marchenko).
27. A. Kheifets, Hamburger moment problem: Parseval equality and A-singularity, J. Funct. Anal. 141 (1996), no. 2, 374-420.
28. A. Kheifets, The abstract interpolation problem and applications, in: Holomorphic spaces (Ed. D. Sarason, S. Axler, J. McCarthy), pages 351-379, Cambridge Univ. Press, Cambridge, 1998.
29. A. Kheifets, Parseval's equality in the abstract interpolation problem and the coupling of open systems. I., Teor. Funktsii, Funktsional. Anal i Prilozhen., 49 (1988), 112-120, 126; English Translation: J. Soviet Math. 49 (1990), 1114-1120.
30. A. Kheifets, Parseval's equality in the abstract interpolation problem and the coupling of open systems. I., Teor. Funktsii, Funktsional. Anal i Prilozhen., 49 (1988), 112-120, 126; English Translation: J. Soviet Math. 49 (1990), 1114-1120.
31. I. V. Kovalishina, Carathéodory-Julia theorem for matrix-functions, Teoriya Funktsii, Funktsianal'nyi Analiz i Ikh Prilozheniya, 43 (1985), 70-82. English translation in: Journal of Soviet Mathematics, 48(2) (1990), 176-186.
32. I. V. Kovalishina, Carathéodory-Julia theorem for matrix-functions, Teoriya Funktsii, Funktsianal'nyi Analiz i Ikh Prilozheniya, 43 (1985), 70-82. English translation in: Journal of Soviet Mathematics, 48(2) (1990), 176-186.
33. S. McCullough, The local de Branges-Rovnyak construction and complete Nevanlinna-Pick kernels, in Algebraic methods in operator theory (Ed. R. Curto and P. E. T. Jorgensen), Birkhäuser-Verlag, Boston, 1994, pp. 15-24.
34. G. Popescu, Interpolation problems in several variables, J. Math. Anal. Appl., 227 (1998), 227-250.
35. P. Quiggin, For which reproducing kernel Hubert spaces is Pick's theorem true? Integral Equations Operator Theory 16 (1993), no. 2, 244-266.
36. I. V. Kovalishina and V .P. Potapov, Seven Papers Translated from the Russian, Amer. Math. Soc. Transl. (2), 138, Providence, R.I., 1988.
37. R. Nevanlinna, Über beschränkte Funktionen, Ann. Acad. Sci. Fenn. Ser. A 32 (1939), no. 7.
38. M. Rosenblum and J. Rovnyak, Hardy classes and operator theory, Oxford University Press, 1985.
39. n, Springer-Verlag, New York, 1980.
40. D. Sarason, Sub-Hardy Hubert Spaces in the Unit Disk, University of Arkansas Lecture Notes in the Matehmatical Sciences, Wiley, 1994.
41. D. Sarason, Nevanlinna-Pick interpolation with boundary data, Integral Equations and Operator Theory 30(2) (1998), 231-250.