Fredholm Integral Equation of the First Kind

A Fredholm integral equation of the first kind is an integral equation of the form

(1)

where  is the kernel and  is an unknown function to be solved for (Arfken 1985, p. 865).

If the kernel is of the special form  and the limits are infinite so that the equation becomes

(2)

then the solution (assuming the relevant transforms exist) is given by

(3)

where  is the Fourier transforms operator (Arfken 1985, pp. 875 and 877).

REFERENCES:

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, 1985.