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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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.
Editor information
Rights and permissions
Copyright information
© 1975 Springer-Verlag
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/BFb0067109
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07161-7
Online ISBN: 978-3-540-69975-0
eBook Packages: Springer Book Archive