Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
A Characterization Of The Solution Of A Fredholm Integral Equation With L∞ Forcing Term, Hideaki Kaneko, Richard Noren, Yuesheng Xu
A Characterization Of The Solution Of A Fredholm Integral Equation With L∞ Forcing Term, Hideaki Kaneko, Richard Noren, Yuesheng Xu
Mathematics & Statistics Faculty Publications
In this paper we investigate the regularity properties of the Fredholm equation (Formula Presented) . The kernel is the product of the smooth function k and the singular function gα (Formula Presented). The forcing function f is in L∞. We obtain a decomposition of the solution as the sum of two functions—one with a discontinuity reflecting that of the forcing function—and the other a regular function. Our results extend those of C. Schneider [6], who assumes a condition that is stronger than f ∈ C[a, b] ∩ Cm(a,b) (for some integer m). © 1990 …