Authors: by George Gasper and Walter Trebels
Abstract: Let the fractional integration operator $I^{\sigma}$ be generated by the sequence $\{ (k+1)^{-\sigma}\}\, $ in the setting of Laguerre and Hermite expansions. Via projection formulas the problem of the norm boundedness of $I^{\sigma}$ is reduced to well-known fractional integration on the half-line. A corresponding result with respect to the modified Han\-kel transform is derived and its connection with Laguerre fractional integration is indicated.
Key words. Fractional integration, Laguerre and Hermite expansions, Hankel transforms, multipliers
AMS(MOS) subject classifications. 26A33, 33C45, 42A38, 42C10