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Fractional spaces of temperate distribution

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Part of the Lecture Notes in Mathematics book series (LNM,volume 457)

Abstract

The use of fractional derivatives enables a natural construction of a family of Hilbert spaces H, λ ≧ 0, such that the union of all H is the space S'(Rn) of temperate distributions. For each λ ≧ 0 the largest locally convex space Oλ of functions, by which distributions from H can be sensibly multiplied, is defined and the continuity of multiplication on Oλ × H is established.

Keywords

  • Hilbert Space
  • Convex Hull
  • Identity Mapping
  • Fractional Derivative
  • Topological Vector Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. L. Schwartz: Théorie des distributions, Nouvelle édition, Hermann, Paris 1966.

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  2. J.Horváth: Topological Vector Spaces and Distributions, Vol. 1, Addison-Wesley 1966.

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  3. J. Kucera: "Fourier L2-transform of Distributions", Czech. Math. J., Vol. 19(94), Praha 1969, pp. 143–153.

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  4. J. Kucera: "On Multipliers of Temperate Ditributions", Czech. Math. J., Vol. 21(96), Praha 1971, pp. 610–618.

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  5. J.Kucera, K.McKennon: "Certain Topologies on the Space of Temperate Distributions and its Multipliers", Indiana Univ. Math. J., Vol. 23, February 1975.

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© 1975 Springer-Verlag

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Kucera, J. (1975). Fractional spaces of temperate distribution. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067109

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  • DOI: https://doi.org/10.1007/BFb0067109

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07161-7

  • Online ISBN: 978-3-540-69975-0

  • eBook Packages: Springer Book Archive