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Paper ‘On the ideal structure of the Nevanlinna class’

I have published the content of my master thesis (done at Universität Karlsruhe in Germany) as:

Reiner Martin, On the ideal structure of the Nevanlinna class. Proceedings of the American Mathematical Society 114, No. 1, 135-143 (1992). PDF

Abstract

As quoted from the paper: “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.”

Quoted by

  • Meštrović, Romeo, and Žarko Pavićević, A short survey of the ideal structure of Privalov spaces on the unit disk, Mathematica Montisnigri 32 (2015): 14-22, PDF
  • Meštrović, Romeo, and Žarko Pavićević, Algebraic Properties Of Some F-algebras Of Holomorphic Functions, XV International Seminar, PDF
  • Meštrović, Romeo, and Žarko Pavićević, Privalov Spaces On The Unit Disk
  • Hartmann, Andreas, Xavier Massaneda, and Artur Nicolau, Finitely generated ideals in the Nevanlinna class, 2016, arXiv, PDF

Keywords

Ideals; Nevanlinna class; corona property. AMS Classification: 30D50 Blaschke products; 30H05 Spaces and algebras of analytic functions; 46E25 Rings and algebras of functions with smoothness properties.