Good-irreducible inner functions on a polydisc
Annales de l'Institut Fourier, Volume 29 (1979) no. 2, pp. 185-210.

An explicit formula is developed for Nevanlinna class functions whose behaviour at the boundary is “sufficiently rational” and is then used to deduce the uniqueness of the factorization of such inner functions. A generalization of a theorem of Frostman is given and the above results are then applied to the construction of good and/or irreducible inner functions on a polydisc.

Une formule explicite est développée pour les fonctions de classe de Nevanlinna qui sont “suffisamment rationnelles” sur la frontière et elle est alors utilisée pour déduire l’unicité de la factorisation de telles fonctions intérieures. Une généralisation d’un théorème de Frostman est présentée et les résultats ci-dessus sont alors appliqués pour construire des fonctions intérieures irréductibles et/ou “bonnes” sur un polydisque.

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Sawyer, Eric T. Good-irreducible inner functions on a polydisc. Annales de l'Institut Fourier, Volume 29 (1979) no. 2, pp. 185-210. doi : 10.5802/aif.746. http://www.numdam.org/articles/10.5802/aif.746/

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