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Interpolation by Bounded Analytic Functions and Related Questions

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Part of the book series: Fields Institute Communications ((FIC,volume 81))

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Abstract

The paper investigates some interpolation questions related to the Khinchine–Ostrowski theorem, Zalcman’s theorem on bounded approximation, and Rubel’s problem on bounded analytic functions.

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Notes

  1. 1.

    If a closed set E is of positive measure but has a portion of measure zero, then even such a set cannot belong to the class of sets which Problem 2 requires to describe. See Sect. 2 below for the definition of a portion of E.

  2. 2.

    See Sect. 2 for the definition of portion of a closed set.

References

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Acknowledgements

The author wishes to thank the referee for some mathematical and stylistic corrections, and D. Savchuk for preparation of the electronic file of Fig. 1. He also wishes to thank S. Gardiner, V. Totik, and L. Zalcman for valuable discussions related to the topic of this paper.

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Authors and Affiliations

  1. University of South Florida, Tampa, FL, 33620, USA

    Arthur A. Danielyan

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  1. Arthur A. Danielyan
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Correspondence to Arthur A. Danielyan .

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Editors and Affiliations

  1. Département de Mathématiques et de Statistique, Université Laval, Québec, Québec, Canada

    Javad Mashreghi

  2. Department of Mathematics and Statistics, University of South Florida, Tampa, Florida, USA

    Myrto Manolaki

  3. Département de Mathématiques et de Statistique, Université de Montréal, Montreal, Québec, Canada

    Paul Gauthier

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Danielyan, A.A. (2018). Interpolation by Bounded Analytic Functions and Related Questions. In: Mashreghi, J., Manolaki, M., Gauthier, P. (eds) New Trends in Approximation Theory. Fields Institute Communications, vol 81. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7543-3_11

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