Convolutions over Other Intervals

Abstract

The associated Laplace convolution over the interval (x, ∞) has quite different properties from the convolution over the interval (0, x). The Mellin convolution over (0, x) can be converted to a similar equation over (x, ∞). The integral equations of these types are more closely related to convolutions over the intervals (0, ∞), (−∞, +∞) and (a, b). We discuss certain cases of these various convolutions for which the methods of the previous chapters provide explicit solutions. Additional examples of relations between integral equations and functional equations are included. Various results of the types considered in this chapter are listed in Tables 3 through 8.