Handbook of Function and Generalized Function Transformations

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.

Ahmed I. Zayed

1 Preliminaries, 2 Special Functions, 3 Generalized Functions, 4 Function Transformations, 5 The Laplace Transform, 6 The Two-Sided Laplace Transform, 7 The Borel Transform, 8 The Stieltjes Transform, 9 The Lambert Transform, 10 The Mellin Transform, 11 Finite Mellin-Type Transforms, 12 The Fourier Transform, 13 The Hartley Transform, 14 The Hilbert Transform, 15 The Boas Transform, 16 The Mittag-Leffler Transform, 17 The Convolution Transform, 18 The Weierstrass Transform, 19 The Abel Transform, 20 The Riemann-Liouville and Weyl Fractional Integrals, 21 The Hankel and Hankel-Type Transforms, 22 The Hardy Transform, 23 The K (Meijer) Transform, 24 The Kontorovich-Lebedev Transform, 25 The Mehler-Fock Transform, 26 The Sturm-Liouville-Type Transforms, 27 Miscellaneous Transforms, 28 The Bargmann Transform, 29 The Zak Transform, 30 The Gabor Transform, 31 The Ambiguity Transformation and Wigner Distribution, 32 The Wavelet Transform, 33 The Radon Transform, 34 Sequence Transformations, Appendices, A Signal Analysis Terminology, B Tables of Integral Transforms, C List of Symbols, References, Index