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Full Description
This book is concerned with the well-established mathematical technique known as Fourier analysis (or alternatively as harmonic or spectral analysis). It is a handbook comprising a collection of the most important theorems in Fourier analysis, presented without proof in a form that is accurate but also accessible to a reader who is not a specialist mathematician. The technique of Fourier analysis has long been of fundamental importance in the physical sciences, engineering and applied mathematics, and is today of particular importance in communications theory and signal analysis. Existing books on the subject are either rigorous treatments, intended for mathematicians, or are intended for non-mathematicians, and avoid the finer points of the theory. This book bridges the gap between the two types. The text is self-contained in that it includes examples of the use of the various theorems, and any mathematical concepts not usually included in degree courses in physical sciences and engineering are explained. This handbook will be of value to postgraduates and research workers in the physical sciences and in engineering subjects, particularly communications and electronic engineering.
Contents
Preface; 1. Introduction; 2. Lebesque integration; 3. Some useful theorems; 4. Convergence of sequences of functions; 5. Local averages and convolution kernels; 6. Some general remarks on Fourier transformation; 7. Fourier theorems for good functions; 8. Fourier theorems in Lp; 9. Fourier theorems for functions outside Lp; 10. Miscellaneous theorems; 11. Power spectra and Wiener's theorems; 12. Generalized functions; 13. Fourier transformation of generalized function I; 14. Fourier transformation of generalized function II; 15. Fourier series; 16. Generalized Fourier series; Bibliography; Index.
