A Proposal for the Calculation of Characteristic Functions for Certain Differential and Integral Operators Via Initial-Value Procedures

摘要

The Memorandum presents an intital-value method for the solution of the inhomogeneous Fredholm integral equation u(t) = g(t) + (lambda) the integral from 0 to c of (k(the absolute value of (t-y))u(y)dy). These equations and an expansion formula of classical analysis allow a proposal to be made for calculating the solutions to the homogeneous equation phi(t) = (lambda) the integral from 0 to c of (k(the absolute value of (t-y))phi(y)dy). The Memorandum discusses possible numerical difficulties and presents extensions to other types of linear operators. (Author)