Proceedings of the American Mathematical Society

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



On the ideal structure of the Nevanlinna class

Author: Reiner Martin
Journal: Proc. Amer. Math. Soc. 114 (1992), 135-143
MSC: Primary 46J20; Secondary 30H05, 46J15
MathSciNet review: 1069291
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Abstract: Let $ N$ denote the Nevanlinna class, i.e. the algebra of holomorphic functions of bounded characteristic in the open unit disc. We study analytic conditions for a finitely generated ideal to be equal to the whole algebra $ N$. Then we characterize the finitely generated prime ideals containing a nontangential interpolating Blaschke product. Further, we give an example of an ideal of $ N$ whose closure in the natural metric on $ N$ is not an ideal.

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  • [1] Peter L. Duren, Theory of 𝐻^{𝑝} spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
  • [2] John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
  • [3] Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. MR 0133008
  • [4] A. Kerr-Lawson, Some lemmas on interpolating Blaschke products and a correction, Canad. J. Math. 21 (1969), 531–534. MR 0247102
  • [5] Raymond Mortini, Zur Idealstruktur von Unterringen der Nevanlinna-Klasse 𝑁, Travaux mathématiques, I, Sém. Math. Luxembourg, Centre Univ. Luxembourg, Luxembourg, 1989, pp. 81–91 (German). MR 1264197
  • [6] K. V. Rajeswara Rao, On a generalized corona problem, J. Analyse Math. 18 (1967), 277–278. MR 0210910
  • [7] James W. Roberts and Manfred Stoll, Prime and principal ideals in the algebra 𝑁⁺, Arch. Math. (Basel) 27 (1976), no. 4, 387–393. MR 0422639
  • [8] Walter Rudin, Real and complex analysis, 3rd ed., McGraw-Hill, New York, 1986.
  • [9] Joel H. Shapiro and Allen L. Shields, Unusual topological properties of the Nevanlinna class, Amer. J. Math. 97 (1975), no. 4, 915–936. MR 0390227
  • [10] Kenneth Stephenson, Isometries of the Nevanlinna class, Indiana Univ. Math. J. 26 (1977), no. 2, 307–324. MR 0432905
  • [11] Michael von Renteln, Ideals in the Nevanlinna class 𝑁, Mitt. Math. Sem. Giessen Heft 123 (1977), 57–65. Dem Andenken an Karl Maruhn gewidmet. MR 0486534

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Article copyright: © Copyright 1992 American Mathematical Society