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Analytic implementation of the duals of some spaces of infinitely differentiable functions

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Abstract

Using the Fourier-Laplace transform for functionals, we describe the duals of some spaces of the infinitely differentiable functions given on convex compact sets or convex domains in ℝN and such that the growth of their derivatives is determined by weight sequences of a general form.

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Authors and Affiliations

  1. Rostov State University, Rostov-on-Don, Russia

    A. V. Abanin & I. A. Filip’ev

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  1. A. V. Abanin
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  2. I. A. Filip’ev
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Original Russian Text Copyright © 2006 Abanin A. V. and Filip’ev I. A.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 3, pp. 485–500, May–June, 2006.

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Abanin, A.V., Filip’ev, I.A. Analytic implementation of the duals of some spaces of infinitely differentiable functions. Sib Math J 47, 397–409 (2006). https://doi.org/10.1007/s11202-006-0052-3

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  • DOI: https://doi.org/10.1007/s11202-006-0052-3

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