The relation between differential operators and integral transforms is the 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, more.

I. Introduction
II. The Finite Kernels
III. The Non-Finite Kernels
IV. Variation Diminishing Transforms
V. Asymptotic Behaviour of Kernels
VI. Real Inversion Theory
VII. Representation Theory
VIII. The Weierstrass Transform
IX. Complex Inversion Theory
X. Miscellaneous Topics
Bibliography
Symbols and Notations
Index