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Generalized Schur Functions as Multivalent Functions
Complex Analysis and Operator Theory ( IF 0.8 ) Pub Date : 2021-01-14 , DOI: 10.1007/s11785-020-01071-6
Hendrik Luit Wietsma

The multivalency approach to generalized Nevanlinna functions established in Wietsma (Indag Math 29:997–1008, 2018) is here extended to the related class of generalized Schur functions giving thereby rise to new characterizations for this class of functions as well as a straightforward function-theoretical proof of its factorization. In particular, this multivalency approach explains how the well-known factorizations of the two mentioned classes of functions differ from each other. Indeed, by this approach a new factorization of generalized Schur functions is obtained which is more directly connected to the factorization of generalized Nevanlinna functions. These results demonstrate that multivalency is a valuable concept for the complete understanding of the mentioned classes of functions.



中文翻译:

广义Schur函数为多价函数

维茨玛(Indag Math 29:997–1008,2018)中建立的广义Nevanlinna函数的多价方法在此扩展到广义Schur函数的相关类,从而引起此类函数的新表征以及一个简单的函数-其因式分解的理论证明。尤其是,这种多价方法解释了上述两个函数类别的众所周知的分解如何彼此不同。实际上,通过这种方法,获得了广义舒尔函数的新因式分解,该新因式分解更直接地与广义Nevanlinna函数的因式分解相关。这些结果表明,对于完全理解所提到的功能类别,多价是一个有价值的概念。

更新日期:2021-01-14
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