ABSTRACT
In this chapter we present methods for solving Volterra linear equations of the first kind. These equations have the form ∫ x
K(x, t)y(t) dt = f (x), (1)
where y(x) is the unknown function (a ≤ x ≤ b), K(x, t) is the kernel of the integral equation, and f (x) is a given function, the right-hand side of Eq. (1). The functions y(x) and f (x) are usually assumed to be continuous or square integrable on [a, b]. The kernel K(x, t) is usually assumed either to be continuous on the square S = {a ≤ x ≤ b, a ≤ t ≤ b} or to satisfy the condition∫ b
K2(x, t) dx dt = B2 <∞, (2)
where B is a constant, that is, to be square integrable on this square. It is assumed in (2) that K(x, t) ≡ 0 for t > x.
