Sharp bounds for singular values of fractional integral operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:327

Article

Burman, Prabir

关键词: fractional integral operator;    fractional difference;    fractional summation;    singular values;    eigenvalues;   

DOI  :  10.1016/j.jmaa.2006.03.073

来源: Elsevier

【 摘 要 】

From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380-391] and Vu and Gorenflo [Kim Tuan Vu, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174-185] it is known that the jth singular value of the fractional integral operator of order alpha > 0 is approximately (pi j)(-alpha) for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is (pi j)(-alpha)[1 + O(j(-1))]. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free