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Locally Convex Spaces of the Sebastian-e-Silva Type Generated by the Operator of Differentiation

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Abstract

It is established in the paper that the spaces of entire functions of exponential type generated by the operator of differentiation defined in the space of summable functions on the axis belong to the well-known Sebastian-e-Silva class of locally convex spaces. Some properties of the spaces relating to the duality and the open map theorem, as well as properties of convolution, are described.

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  1. Pidstrygach Institute of Applied Problems in Mechanics and Mathematics of the National Academy of Science of Ukraine, Lviv

    V. Ya. Lozynska

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  1. V. Ya. Lozynska
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Lozynska, V.Y. Locally Convex Spaces of the Sebastian-e-Silva Type Generated by the Operator of Differentiation. Journal of Mathematical Sciences 107, 3567–3569 (2001). https://doi.org/10.1023/A:1011986022134

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  • DOI: https://doi.org/10.1023/A:1011986022134

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