Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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 zero-sets of the radial-limit functions of inner functions
HTML articles powered by AMS MathViewer

by Charles L. Belna, Robert D. Berman, Peter Colwell and George Piranian PDF
Trans. Amer. Math. Soc. 347 (1995), 3605-3612 Request permission

Abstract:

A set $E$ on the unit circle is the zero-set of the radial-limit function of some inner function if and only if $E$ is a countable intersection of ${F_\sigma }$-sets of measure $0$.
References
  • Robert D. Berman, The sets of fixed radial limit value for inner functions, Illinois J. Math. 29 (1985), no. 2, 191–219. MR 784519
  • Robert D. Berman and Togo Nishiura, Some mapping properties of the radial-limit function of an inner function, J. London Math. Soc. (2) 52 (1995), no. 2, 375–390. MR 1356149, DOI 10.1112/jlms/52.2.375
  • G. T. Cargo, Some topological analogues of the F. Riesz and M. Riesz uniqueness theorem, J. London Math. Soc. (2) 12 (1975/76), no. 1, 67–74. MR 390223, DOI 10.1112/jlms/s2-12.1.67
  • E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999
  • P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), no. 1, 335–400 (French). MR 1555035, DOI 10.1007/BF02418579
  • A. J. Lohwater and G. Piranian, The boundary behavior of functions analytic in a disk, Ann. Acad. Sci. Fenn. Ser. A. I. 1957 (1957), no. 239, 17. MR 91342
  • I. I. Priwalow, Randeigenschaften analytischer Funktionen, Hochschulbücher für Mathematik, Band 25, VEB Deutscher Verlag der Wissenschaften, Berlin, 1956 (German). Zweite, unter Redaktion von A. I. Markuschewitsch überarbeitete und ergänzte Auflage. MR 0083565
  • F. Riesz and M. Riesz, Über die Randwerte einer analytischen Funktion, Quatrième Congrès des Math. Scand., 1916, pp. 27-44. W. Sierpiński, Sur une classification des ensembles mesurables (B), Fund. Math. 10 (1927), 320-327.
  • A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 30D40, 30D50
  • Retrieve articles in all journals with MSC: 30D40, 30D50
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 3605-3612
  • MSC: Primary 30D40; Secondary 30D50
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1308000-7
  • MathSciNet review: 1308000