Sharp bounds for singular values of fractional integral operators (Q860567)

The author obtains sharp bounds on the singular values of the fractional integral operator of order greater than 0 which refine the results of \textit{M. R. Dostanić} [J. Math. Anal. Appl. 175, No. 2, 380--391 (1993; Zbl 0777.45006)], \textit{Kim Tuan Vu} and \textit{R. Gorenflo} [in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Min City, 1995, Ho Chi Min City Math. Soc., 174--185 (1995; Zbl 0829.45001)]. The bounds on the singular values are obtained by approximating the fractional integral operator by fractional summation operators for which sharp bound are known of \textit{P. Burman} [Linear Algebra Appl. 416, No. 2--3, 677--687 (2006; Zbl 1101.15013)]. As a by-product the author also obtains the error rate for approximating the singular values of a fractional operator by those of the fractional summation operator.