Integral Equations with Convolution Kernels

Uniqueness of Fixed Momentum Transfer Amplitudes Derived from Data

“…One can easily verify that the kernel of the singular integral equation ( 12) is not of the Fredholm type [8]. Atkinson and Contogouris [9] have considered integral equations with a similar type of singularity.…”

“…From the definition of eZ(z) it follows that K2 is a compact or completely continuous operator [8]. In order to show this we divide the kernel K2 into two parts by truncating the series expansion of (1 -zz')-l after L terms L -1 In the estimate we have used the identity dz ' 1 where S(z) and thus D(z) are given.…”

Global existence and estimates of the solutions to nonlinear integral equations

“…There is a large literature on nonlinear integral equations, [1], [6]. The usual methods to study such equations include fixed-point theorems such as contraction mapping principle and degree theory, (Schauder and Leray-Schauder theorems).…”