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The transforms and applications handbook. (English) Zbl 0851.44001

The Electrical Engineering Handbook Series. Aylesfort: CRC Press. New York, NY: IEEE Press, vii, 1103 p. (1996).
This handbook is published by CRC Press in cooperation with IEEE Press, which underlines its orientation towards electrical engineers. It can also be very useful to all individuals related to applied mathematics and physics. The main value of the book is that it brings together all transforms important in practice. These transforms are presented in twelve articles, written by different authors. Here are the titles:
1. Signals and systems (A. D. Poularikas, pp. 1-94); 2. Fourier transforms (K. B. Howell, pp. 95-225); 3. Sine and cosine transforms (Pat Yip, pp. 227-280); The Hartley transform (K. J. Oleiniczak, pp. 281-330); 5. Laplace transforms (S. Seely, 331-386); 6. The \(Z\)-transform (A. D. Poularikas, pp. 387-461); 7. Hilbert transforms (S. L. Hahn, pp. 463-629); 8. Radon and Abel transforms (S. R. Deans, pp. 631-717); 9. The Hankel transform (R. Piessens, pp. 719-745); 10. Wavelet transform (Y. Sheng, pp. 747-827); 11. The Mellin transform (J. Bertrand, P. Bertrand and J.-P. Ovarles, pp. 829-885); 12. Mixed time-frequency signal transformations (G. Fay Boudreaux-Bartels, pp. 887-892).
The first chapter is introductory, providing a short overview of transforms and some special functions. All articles contain an introduction, definitions, examples, short tables and further references. At the end of the book one finds several helpful appendices (Functions of complex variables, Series and summation, Definite integrals, Matrices and determinants, Vector analysis, Algebra formulas and coordinate systems).
Reviewer’s remark: Some articles contain a reference to the well-known Bateman Manuscript project, cf. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi [Tables of integral transforms. Vol. I (1954; Zbl 0055.36401), Vol. II (1954; Zbl 0058.34103)]. However, references to some more recent important titles are missing. The readers will greatly benefit if references to the following books and tables are included in the next edition, especially in articles 2, 3, 5.
1. Yu. A. Brychkov and A. P. Prudnikov, Integral transforms of generalized functions, Gordon and Breach (1989; Zbl 0729.46016).
2. D. G. Duffy, Transform methods for solving partial differential equations, CRC Press (1994).
3. I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products, Academic Press (1980; Zbl 0521.33001).
4. F. Oberhettinger, Tables of Fourier transforms and Fourier transforms of distributions, Springer-Verlag (1990; Zbl 0694.42017).
5. A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, Integrals and series, Vol. 4: Direct Laplace transforms (1992; Zbl 0786.44003) and Vol. 5: Inverse Laplace transforms, Gordon and Breach (1992; Zbl 0781.44002). (These are apparently the most complete Laplace transform tables in print).

MSC:

44-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral transforms
00A20 Dictionaries and other general reference works
65T50 Numerical methods for discrete and fast Fourier transforms
44A10 Laplace transform
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
78-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to optics and electromagnetic theory
44A15 Special integral transforms (Legendre, Hilbert, etc.)
44A12 Radon transform
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