Theory of Fourier Integrals

Theory of Fourier Integrals

1938 | Prof. E. C. Titchmarsh
The passage discusses the comprehensive and detailed work on the classification and description of 76 species, highlighting the thoroughness of the authors' studies. It mentions the distribution of species among sections, the provision of elaborate keys for identification, and the inclusion of detailed descriptions and plates for each species. The text also covers dialect names, economic uses, and geographical distribution, with specific attention to the removal of toxins in food preparation. The production of plates, some by native artists and others by experts, is noted, along with the financial support from the Bentham-Moxon fund. The second part introduces a book by Prof. E. C. Titchmarsh on the theory of Fourier integrals. The book meets the demand for a comprehensive treatment of trigonometric integrals, following Prof. Zygmund's "Trigonometric Series." It covers the theory of Fourier transforms in the class \(L^2\), emphasizing Plancherel's theorem and its various proofs. The book also discusses Fourier transforms in \(L^p\) classes, the general theory of transforms, and the theory of conjugate functions. Applications to differential and integral equations, as well as probability and statistical dynamics, are covered. The book concludes with a bibliography, and it is praised for its depth and clarity, though it focuses primarily on the theoretical aspects rather than recent specialized developments.The passage discusses the comprehensive and detailed work on the classification and description of 76 species, highlighting the thoroughness of the authors' studies. It mentions the distribution of species among sections, the provision of elaborate keys for identification, and the inclusion of detailed descriptions and plates for each species. The text also covers dialect names, economic uses, and geographical distribution, with specific attention to the removal of toxins in food preparation. The production of plates, some by native artists and others by experts, is noted, along with the financial support from the Bentham-Moxon fund. The second part introduces a book by Prof. E. C. Titchmarsh on the theory of Fourier integrals. The book meets the demand for a comprehensive treatment of trigonometric integrals, following Prof. Zygmund's "Trigonometric Series." It covers the theory of Fourier transforms in the class \(L^2\), emphasizing Plancherel's theorem and its various proofs. The book also discusses Fourier transforms in \(L^p\) classes, the general theory of transforms, and the theory of conjugate functions. Applications to differential and integral equations, as well as probability and statistical dynamics, are covered. The book concludes with a bibliography, and it is praised for its depth and clarity, though it focuses primarily on the theoretical aspects rather than recent specialized developments.
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[slides and audio] Introduction to the Theory of Fourier Integrals