Handbook of Function and Generalized Function Transformations
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Summary
Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems.
The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included.
The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations. It is organized for convenient reference, with chapters broken down into the following sections:
Table of Contents
Preliminaries
Special Functions
Generalized Functions
Function Transformations
The Laplace Transform
The Two-Sided Laplace Transform
The Borel Transform
The Stieltjes Transform
The Lambert Transform
The Mellin Transform
The Mellin-Type Transform
The Fourier Transform
The Hartley Transform
The Hilbert Transform
The Boas Transform
The Mittag-Leffler Transform
The Convolution Transform
The Weierstrass Transform
The Abel Transform
The Riemann-Liouville and Weyl Fractional Integrals
The Hankel and Hankel-Type Transforms (The I, Y and H-Transforms)
The Hardy Transform
The K(Meijer)-Transform
The Kontorovich-Lebedev Transform
The Mehler-Fock Transform
The Sturm-Liouville-Type Transforms
Miscellaneous Transforms: Kummer, Erdelyi, Hypergeometric, E, and G Transforms
The Bargmann Transform
The Zak Transform
The Gabor Transform
The Ambiguity Transformation and Wigner Distribution
The Wavelet Transform
The Radon Transform
Sequence Transformations: The Discrete Fourier, Fast Fourier, Z, and Walsh Transforms
