Skip to Main Content

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)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The Schur algorithm and coefficient characterizations for generalized Schur functions
HTML articles powered by AMS MathViewer

by Tiberiu Constantinescu and Aurelian Gheondea PDF
Proc. Amer. Math. Soc. 128 (2000), 2705-2713 Request permission

Abstract:

In this paper we analyze the existence of a Schur algorithm and obtain coefficient characterizations for the functions in a generalized Schur class. An application to an interpolation problem of Carathéodory type raised by M.G. Kreĭn and H. Langer is indicated.
References
  • V. M. Adamjan, D. Z. Arov, and M. G. Kreĭn, Analytic properties of the Schmidt pairs of a Hankel operator and the generalized Schur-Takagi problem, Mat. Sb. (N.S.) 86(128) (1971), 34–75 (Russian). MR 0298453
  • D. Alpay, A. Dijksma, J. Rovnyak, H.S.V. de Snoo: Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces, Birkhäuser, Basel-Boston-Berlin, 1996.
  • T. Ya. Azizov and I. S. Iokhvidov, Linear operators in spaces with an indefinite metric, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1989. Translated from the Russian by E. R. Dawson; A Wiley-Interscience Publication. MR 1033489
  • Joseph A. Ball and J. William Helton, A Beurling-Lax theorem for the Lie group $\textrm {U}(m,\,n)$ which contains most classical interpolation theory, J. Operator Theory 9 (1983), no. 1, 107–142. MR 695942
  • Gene Christner and James Rovnyak, Julia operators and the Schur algorithm, Harmonic analysis and operator theory (Caracas, 1994) Contemp. Math., vol. 189, Amer. Math. Soc., Providence, RI, 1995, pp. 135–160. MR 1347011, DOI 10.1090/conm/189/02261
  • Tiberiu Constantinescu and Aurelian Gheondea, Minimal signature in lifting of operators. II, J. Funct. Anal. 103 (1992), no. 2, 317–351. MR 1151551, DOI 10.1016/0022-1236(92)90124-2
  • T. Constantinescu, A. Gheondea: Kolmogorov decompositions and the realization of time dependent systems, preprint 1997.
  • I. S. Iohvidov and M. G. Kreĭn, Spectral theory of operators in spaces with indefinite metric. II, Trudy Moskov. Mat. Obšč. 8 (1959), 413–496 (Russian). MR 0107821
  • M. G. Kreĭn and H. Langer, Über die verallgemeinerten Resolventen und die charakteristische Funktion eines isometrischen Operators im Raume $\Pi _{\kappa }$, Hilbert space operators and operator algebras (Proc. Internat. Conf., Tihany, 1970) Colloq. Math. Soc. János Bolyai, vol. 5, North-Holland, Amsterdam, 1972, pp. 353–399 (German). MR 0423122
  • M. G. Kreĭn and H. Langer, Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume $\Pi _{\kappa }$ zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen, Math. Nachr. 77 (1977), 187–236. MR 461188, DOI 10.1002/mana.19770770116
  • M. G. Kreĭn and A. A. Nudel′man, The Markov moment problem and extremal problems, Translations of Mathematical Monographs, Vol. 50, American Mathematical Society, Providence, R.I., 1977. Ideas and problems of P. L. Čebyšev and A. A. Markov and their further development; Translated from the Russian by D. Louvish. MR 0458081
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30C50, 47B50, 30E05
  • Retrieve articles in all journals with MSC (1991): 30C50, 47B50, 30E05
Additional Information
  • Tiberiu Constantinescu
  • Affiliation: Department of Mathematics, University of Texas at Dallas, Richardson, Texas 75083-0688
  • Email: tiberiu@utdallas.edu
  • Aurelian Gheondea
  • Affiliation: Institutul de Matematică al Academiei Române, CP 1-764, 70700 Bucureşti, România
  • Email: gheondea@imar.ro
  • Received by editor(s): March 30, 1998
  • Received by editor(s) in revised form: October 29, 1998
  • Published electronically: February 28, 2000
  • Additional Notes: The second author’s research was partially supported by the Ministry of Research and Technology of Romania grant 4022GR/1998.
  • Communicated by: David R. Larson
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 2705-2713
  • MSC (1991): Primary 30C50, 47B50, 30E05
  • DOI: https://doi.org/10.1090/S0002-9939-00-05375-2
  • MathSciNet review: 1670430