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On the tangential interpolation problem for matrix-valued  -functions of two variables
Author(s):
D.
Alpay;
V.
Bolotnikov
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1789-1799.
MSC (1991):
Primary 41A05, 32A35
Posted:
February 17, 1999
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Abstract:
All solutions of a general tangential interpolation problem for matrix-valued Hardy functions of two variables are described. The minimal norm solution is explicitly expressed in terms of the interpolation data.
References:
- 1.
- J. Agler. Some interpolation theorems of Nevanlinna-Pick type. Preprint.
- 2.
- D. Alpay and V. Bolotnikov. Two-sided interpolation for matrix functions with entries in the Hardy space. Linear Algebra Appl., 223/224:31-56, 1995. MR 96h:47020
- 3.
- D. Alpay and V. Bolotnikov. On tangential interpolation in reproducing kernel Hilbert space modules and applications. In H. Dym, B. Fritzsche, V. Katsnelson, and B. Kirstein, editors, Topics in interpolation theory, volume 95 of Operator Theory: Advances and Applications, pages 37-68. Birkhäuser Verlag, Basel, 1997.
- 4.
- D. Alpay, V. Bolotnikov, and Ph. Loubaton. On two sided residue interpolation for
 functions with symmetries. J. Math. Anal. Appl., 200:76-105, 1996. - 5.
- J. Ball, I. Gohberg, and L. Rodman. Interpolation of rational matrix functions. Birkhäuser Verlag, Basel, 1990. MR 92m:47027
- 6.
- J. Ball and T.Trent. Unitary colligations, reproducing kernel Hilbert spaces and Nevanlinna-Pick interpolation in several variables. Preprint, 1996.
- 7.
- J. Dieudonné. Eléments d'analyse, Volume 1: fondements de l'analyse moderne. Gauthier-Villars, Paris, 1969. MR 38:4246
- 8.
- H. Dym.
 contractive matrix functions, reproducing kernel spaces and interpolation, volume 71 of CBMS Lecture Notes. Amer. Math. Soc., Rhodes Island, 1989. MR 90j:47003 - 9.
- H. Dym. Book review on the book: The commutant lifting approach to interpolation problems, by C. Foias and A. Frazho. Bulletin of the A.M.S., 31(1):1-16, 1994.
- 10.
- C. Foias and A. Frazho. The commutant lifting approach to interpolation problems, volume 44 of Operator Theory: Advances and Applications. Birkhäuser Verlag, Basel, 1990. MR 92k:47033
- 11.
- H. Meschkovski. Hilbertsche Räume mit Kernfunktion. Springer-Verlag, 1962.
- 12.
- R.A. Penrose. A generalized inverse for matrices. Proceedings Cambridge Phil. Soc., 51:406-413, 1955. MR 16:1082a
- 13.
- W. Rudin. Function theory in polydisks. W.A. Benjamin, New-York, 1969. MR 41:501
- 14.
- I. Schur. Über die Potenzreihen, die im Innern des Einheitkreises beschränkten sind, I. Journal fur die reine und angewandte Mathematik, 147, 1917. English translation in: I. Schur methods in operator theory and signal processing. (Operator theory: Advances and Applications OT 18 (1986), Birkhäuser Verlag), Basel. MR 88d:00006
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Additional Information:
D.
Alpay
Affiliation:
Department of Mathematics, Ben--Gurion University of the Negev, Beer-Sheva 84105, Israel
V.
Bolotnikov
Affiliation:
Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
DOI:
10.1090/S0002-9939-99-04651-1
PII:
S 0002-9939(99)04651-1
Received by editor(s):
June 25, 1997
Received by editor(s) in revised form:
September 17, 1997
Posted:
February 17, 1999
Communicated by:
Theodore W. Gamelin
Copyright of article:
Copyright
1999,
American Mathematical Society
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