Abstract
The use of fractional derivatives enables a natural construction of a family of Hilbert spaces H-λ, λ ≧ 0, such that the union of all H-λ 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-λ can be sensibly multiplied, is defined and the continuity of multiplication on Oλ × H-λ is established.
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References
L. Schwartz: Théorie des distributions, Nouvelle édition, Hermann, Paris 1966.
J.Horváth: Topological Vector Spaces and Distributions, Vol. 1, Addison-Wesley 1966.
J. Kucera: "Fourier L2-transform of Distributions", Czech. Math. J., Vol. 19(94), Praha 1969, pp. 143–153.
J. Kucera: "On Multipliers of Temperate Ditributions", Czech. Math. J., Vol. 21(96), Praha 1971, pp. 610–618.
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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