Abstract
We construct families of universal Taylor series on Ω depending on a parameter w ∈ G, where Ω and G are planar simply connected domains. The functions to be approximated depend on the parameter w, w ∈ G. The partial sums implementing the universal approximation are one variable partial sums with respect to z ∈ Ω for each fixed value of the parameter w ∈ G. The universal approximation extends to mixed partial derivatives. This phenomenon is generic in H( Ω × G).
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Acknowledgements
The authors are grateful to the referee for a careful reading of the manuscript and for his comments, which helped to improve the presentation considerably. Moreover, the authors thank N. Daras for a helpful communication. The work was supported by the Russian Science Foundation (Grant No. 14-41-00010).
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Abakumov, E., Müller, J., Nestoridis, V. (2018). Families of Universal Taylor Series Depending on a Parameter. 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_10
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DOI: https://doi.org/10.1007/978-1-4939-7543-3_10
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