Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the tangential interpolation problem
for matrix-valued $\mathbf{H}_2$-functions of two variables


Authors: D. Alpay and V. Bolotnikov
Journal: Proc. Amer. Math. Soc. 127 (1999), 1789-1799
MSC (1991): Primary 41A05, 32A35
Published electronically: February 17, 1999
MathSciNet review: 1476113
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. J. Agler. Some interpolation theorems of Nevanlinna-Pick type. Preprint.
  • 2. Daniel Alpay and Vladimir Bolotnikov, Two-sided interpolation for matrix functions with entries in the Hardy space, Linear Algebra Appl. 223/224 (1995), 31–56. Special issue honoring Miroslav Fiedler and Vlastimil Pták. MR 1340682 (96h:47020), http://dx.doi.org/10.1016/0024-3795(94)00074-N
  • 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 ${H}_2$ functions with symmetries. J. Math. Anal. Appl., 200:76-105, 1996.
  • 5. Joseph A. Ball, Israel Gohberg, and Leiba Rodman, Interpolation of rational matrix functions, Operator Theory: Advances and Applications, vol. 45, Birkhäuser Verlag, Basel, 1990. MR 1083145 (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, Éléments d’analyse. Tome I: Fondements de l’analyse moderne, Traduit de l’anglais par D. Huet. Avant-propos de G. Julia. Nouvelle édition revue et corrigée. Cahiers Scientifiques, Fasc. XXVIII, Gauthier-Villars, Éditeur, Paris, 1968 (French). MR 0235945 (38 #4246)
  • 8. Andrzej Sołtysiak, On joint spectra of operators on a Banach space isomorphic to its square, Colloq. Math. 57 (1989), no. 2, 331–337. MR 1028865 (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. Ciprian Foias and Arthur E. Frazho, The commutant lifting approach to interpolation problems, Operator Theory: Advances and Applications, vol. 44, Birkhäuser Verlag, Basel, 1990. MR 1120546 (92k:47033)
  • 11. H. Meschkovski. Hilbertsche Räume mit Kernfunktion. Springer-Verlag, 1962.
  • 12. R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406–413. MR 0069793 (16,1082a)
  • 13. Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841 (41 #501)
  • 14. I. Gohberg (ed.), I. Schur methods in operator theory and signal processing, Operator Theory: Advances and Applications, vol. 18, Birkhäuser Verlag, Basel, 1986. MR 902600 (88d:00006)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 41A05, 32A35

Retrieve articles in all journals with MSC (1991): 41A05, 32A35


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: http://dx.doi.org/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
Published electronically: February 17, 1999
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society