|
The Convolution Transform
by Isidore Isaac Hirschman,David V. Widder
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.
Table of Contents for The Convolution Transform
| 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 |
|
 |
|
|