Description
DOVER PUBLICATIONS Convolution Transform by ISIDORE ISAAC HIRSCHMAN
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, which is geared toward upper-level undergraduates and graduate students. It may be read easily by anyone with a working knowledge of real and complex variable theory. Topics include the finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, and complex inversion theory. I. IntroductionII. The Finite KernelsIII. The Non-Finite KernelsIV. Variation Diminishing TransformsV. Asymptotic Behaviour of KernelsVI. Real Inversion TheoryVII. Representation TheoryVIII. The Weierstrass TransformIX. Complex Inversion TheoryX. Miscellaneous TopicsBibliographySymbols and NotationsIndex