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.

 

A formula by V. M. Adamjan, D. Z. Arov and M. G. Kreĭn
HTML articles powered by AMS MathViewer

by Arne Stray PDF
Proc. Amer. Math. Soc. 83 (1981), 337-340 Request permission

Abstract:

For $F$ in ${L^\infty }$ of the unit circle, Adamjan, Arov and Krein obtained a formula describing all functions in the coset $F + {H^\infty }$ of norms not exceeding 1. A proof of this result using classical ideas of Nevanlinna and Schur is given.
References
  • V. M. Adamjan, D. Z. Arov, and M. G. Kreĭn, Infinite Hankel matrices and generalized problems of Carathéodory-Fejér and F. Riesz, Funkcional. Anal. i Priložen. 2 (1968), no. 1, 1–19 (Russian). MR 0234274
    • —, Infinite Hankel matrices and generalized problems of Caratheodory-Fejér and I. Schur, Functional Anal. Appl. 2 (1968), 269-281. —, Analytic properties of Hilbert-Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem, Mat. USSR Sb. 15 (1971), 31-73.
  • Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
  • John B. Garnett, Two remarks on interpolation by bounded analytic functions, Banach spaces of analytic functions (Proc. Pelczynski Conf., Kent State Univ., Kent, Ohio, 1976) Lecture Notes in Math., Vol. 604, Springer, Berlin, 1977, pp. 32–40. MR 0486536
  • Maurice Heins, On WSN functions and a theorem of R. Nevanlinna concerning bounded analytic functions, K\B{o}dai Math. Sem. Rep. 26 (1974/75), 245–257. MR 382652
    • R. Nevanlinna, Über beschränkte Funktionen die in gegebenen Punkten vorgeschribene Werte annehmen, Ann. Acad. Sci. Fenn. Ser. B 15 (1919), 1-71. —, Über beschränkte analytische Funktionen, Ann. Acad. Sci. Fenn. Ser. A 32 (1929), 1-75. I. Schur, Über Potenzreihen, die im Inneren des Einheitskreise beschränkt sind I, J. Math. 147 (1917), 205-232. —, Über Potenzreihen, die im Inneren des Einheitskreise beschränkt sind I, J. Math. 148 (1918), 122-145.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D50, 30E05
  • Retrieve articles in all journals with MSC: 30D50, 30E05
Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 337-340
  • MSC: Primary 30D50; Secondary 30E05
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0624925-5
  • MathSciNet review: 624925