This book is concerned with the well-established mathematical technique known as Fourier analysis (or alternately 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.
This book is concerned with the well-established mathematical technique known as Fourier analysis (or alternately 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.
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.
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.
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