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A Class of Functions Holomorphic in the Disk

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Abstract

We introduce a new parametric representation of the class of holomorphic functions in the unit disk such that their Nevanlinna characteristic has a power growth near the boundary of the disk. The parameters of the obtained representation are determined explicitly by values of the function. In addition, the set of multipliers from the considered class to the Hardy and Bergman classes and the disk algebra is described completely. Bibliography: 10 titles.

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REFERENCES

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Shamoyan, F.A., Shubabko, E.N. A Class of Functions Holomorphic in the Disk. Journal of Mathematical Sciences 120, 1784–1790 (2004). https://doi.org/10.1023/B:JOTH.0000018875.84513.27

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  • DOI: https://doi.org/10.1023/B:JOTH.0000018875.84513.27

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