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A uniqueness result on boundary interpolation
Author(s):
Vladimir
Bolotnikov
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1705-1715.
MSC (2000):
Primary 47A57
Posted:
November 28, 2007
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Abstract:
Let  be an analytic function mapping the unit disk  into itself. We give necessary and sufficient conditions on the local behavior of  near a finite set of boundary points that require  to be a finite Blaschke product.
References:
-
- 1.
- J. A. Ball,
Interpolation problems of Pick-Nevanlinna and Loewner type for meromorphic matrix functions,
Integral Equations Operator Theory 6 (1983), 804-840. MR 719106 (85k:30054) - 2.
- J.A. Ball, I. Gohberg and L. Rodman, Interpolation of Rational Matrix Functions, OT45, Birkhäuser-Verlag, Basel-Boston, 1990. MR 1083145 (92m:47027)
- 3.
- J. A. Ball and J. W. Helton,
Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix-functions: parametrization of the set of all solutions,
Integral Equations Operator Theory 9 (1986), 155-203. MR 837514 (87j:30085) - 4.
- V. Bolotnikov and H. Dym, On boundary interpolation for matrix valued Schur functions, Mem. Amer. Math. Soc. 181 (2006), no. 856. MR 2214130 (2007g:47022)
- 5.
- V. Bolotnikov and A. Kheifets, A higher order analogue of the Carathéodory-Julia theorem, J. Funct. Anal. 237 (2006), no. 1, 350-371. MR 2239269 (2007d:46023)
- 6.
- V. Bolotnikov and A. Kheifets, The higher order Carathéodory-Julia theorem and related boundary interpolation problems, Oper. Theory: Adv. Appl. OT 179, pages 63-102, Birkhäuser-Verlag, Basel, 2007.
- 7.
- V. Bolotnikov and A. Kheifets, Boundary Nevanlinna-Pick interpolation problems for generalized Schur functions, in Interpolation, Schur Functions and Moment Problems (D. Alpay and I. Gohberg, Eds.), Oper. Theory: Adv. Appl. OT 165, pages 67-119, Birkhäuser-Verlag, Basel, 2006. MR 2222520 (2007d:30027)
- 8.
- V. Bolotnikov and L. Rodman, Krein-Langer factorizations via pole triples, Integral Equations Operator Theory 47 (2003), no. 2, 169-195. MR 2002664 (2004h:47021)
- 9.
- L. de Branges and J. Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York, 1966. MR 0215065 (35:5909)
- 10.
- D. Burns and S. G. Krantz, Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary, J. Amer. Math. Soc. 7 (1994), no. 3, 661-676. MR 1242454 (94j:32016)
- 11.
- D. Chelst, A generalized Schwarz lemma at the boundary, Proc. Amer. Math. Soc. 129 (2001), no. 11, 3275-3278. MR 1845002 (2002c:30033)
- 12.
- C. Carathéodory,
Über die Winkelderivierten von beschränkten Funktionen, Sitzungber. Preuss. Akad. Wiss. (1929), 39-52. - 13.
- I. V. Kovalishina, Multiple boundary interpolation problem for contractive matrix-valued functions in the unit circle, J. Soviet Math. 52 (6), (1990), 3467-3481. MR 1009144 (90i:41007)
- 14.
- G. Pick, Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktionswerte bewirkt werden, Math. Ann. 77 (1916), no. 1, 7-23. MR 1511844
- 15.
- D. Sarason,
Nevanlinna-Pick interpolation with boundary data,
Integral Equations Operator Theory 30 (1998), no. 2, 231-250. MR 1607902 (98m:47017) - 16.
- I. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind, J. Reine Angew. Math. 147 (1917), 205-232.
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Additional Information:
Vladimir
Bolotnikov
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795
DOI:
10.1090/S0002-9939-07-09126-5
PII:
S 0002-9939(07)09126-5
Received by editor(s):
January 10, 2006
Received by editor(s) in revised form:
February 20, 2007
Posted:
November 28, 2007
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2007,
American Mathematical Society
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