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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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On the tangential interpolation problem for matrix-valued $\mathbf {H}_2$-functions of two variables
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by D. Alpay and V. Bolotnikov
Proc. Amer. Math. Soc. 127 (1999), 1789-1799
DOI: https://doi.org/10.1090/S0002-9939-99-04651-1
Published electronically: 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
  • J. Agler. Some interpolation theorems of Nevanlinna–Pick type. Preprint.
  • 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 PtĂĄk. MR 1340682, DOI 10.1016/0024-3795(94)00074-N
  • 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. BirkhĂ€user Verlag, Basel, 1997.
  • 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.
  • Joseph A. Ball, Israel Gohberg, and Leiba Rodman, Interpolation of rational matrix functions, Operator Theory: Advances and Applications, vol. 45, BirkhĂ€user Verlag, Basel, 1990. MR 1083145, DOI 10.1007/978-3-0348-7709-1
  • J. Ball and T.Trent. Unitary colligations, reproducing kernel Hilbert spaces and Nevanlinna–Pick interpolation in several variables. Preprint, 1996.
  • J. DieudonnĂ©, ÉlĂ©ments d’analyse. Tome I: Fondements de l’analyse moderne, Cahiers Scientifiques, Fasc. XXVIII, Gauthier-Villars, Éditeur, Paris, 1968 (French). Traduit de l’anglais par D. Huet; Avant-propos de G. Julia; Nouvelle Ă©dition revue et corrigĂ©e. MR 0235945
  • Andrzej SoƂtysiak, On joint spectra of operators on a Banach space isomorphic to its square, Colloq. Math. 57 (1989), no. 2, 331–337. MR 1028865, DOI 10.4064/cm-57-2-331-337
  • 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.
  • Ciprian Foias and Arthur E. Frazho, The commutant lifting approach to interpolation problems, Operator Theory: Advances and Applications, vol. 44, BirkhĂ€user Verlag, Basel, 1990. MR 1120546, DOI 10.1007/978-3-0348-7712-1
  • H. Meschkovski. Hilbertsche RĂ€ume mit Kernfunktion. Springer–Verlag, 1962.
  • Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946
  • Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
  • I. Gohberg (ed.), I. Schur methods in operator theory and signal processing, Operator Theory: Advances and Applications, vol. 18, BirkhĂ€user Verlag, Basel, 1986. MR 902600, DOI 10.1007/978-3-0348-5483-2
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Bibliographic Information
  • D. Alpay
  • Affiliation: Department of Mathematics, Ben–Gurion University of the Negev, Beer-Sheva 84105, Israel
  • MR Author ID: 223612
  • V. Bolotnikov
  • Affiliation: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
  • MR Author ID: 266846
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 1789-1799
  • MSC (1991): Primary 41A05, 32A35
  • DOI: https://doi.org/10.1090/S0002-9939-99-04651-1
  • MathSciNet review: 1476113