Hirschman I.I., Widder D.V. The Convolution Transform

Princeton: Princeton University Press, 2005. — 274 p.In studies of general operators of the same nature, general convolution transforms are immediately encountered as the objects of inversion. The relation between differential operators and integral transforms is the basic theme of this work. Discusses finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, and complex inversion theory.