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|a Bhatia, Rajendra.
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|a Fourier Series /
|c Rajendra Bhatia.
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|a Cambridge :
|b Cambridge University Press,
|c 2012.
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|a Copyright page -- title page -- Contents -- Preface -- 0 A History of Fourier Series -- 1. The motion of a vibrating string -- 2. J. D�Alembert -- 3. L. Euler -- 4. D. Bernoulli -- 5. J. Fourier -- 6. P. Dirichlet -- 7. B. Riemann -- 8. P. du Bois-Reymond -- 9. G. Cantor -- 10. L. Fejér -- 11. H. Lebesgue -- 12. A.N. Kolmogorov -- 13. L. Carleson -- 14. The L_2 theory and Hilbert spaces -- 15. Some modern developments�I -- 16. Some modern developments�II -- 17. Pure and applied mathematics -- Chapt 1 Heat Conduction and Fourier Series
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| 505 |
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|a 1.1 The Laplace equation in two dimensions1.2 Solutions of the Laplace equation -- 1.3 The complete solution of the Laplace equation -- 2 Convergence of Fourier Series -- 2.1 Abel summability and Cesà ro summability -- 2.2 The Dirichlet and the Fejér kernels -- 2.3 Pointwise convergence of Fourier series -- 2.4 Term by term integration and differentiation -- 2.5 Divergence of Fourier series -- 3 Odds and Ends -- 3.1 Sine and cosine series -- 3.2 Functions with arbitrary periods -- 3.3 Some simple examples -- 3.4 Infinite products
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| 505 |
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|a 3.5 π and infinite series3.6 Bernoulli numbers -- 3.7 sinx/x -- 3.8 The Gibbs phenomenon -- 3.9 Exercises -- 3.10 A historical digression -- 4 Convergence in L_2 and L_1 -- 4.1 L_2 convergence of Fourier series -- 4.2 Fourier coefficients of L_1 functions -- 5 Some Applications -- 5.1 An ergodic theorem and number theory -- 5.2 The isoperimetric problem -- 5.3 The vibrating string -- 5.4 Band matrices -- A A Note on Normalisation -- B A Brief Bibliography -- Analysis -- Fourier series -- General reading -- History and biography -- Index
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|a Bhatia, Rajendra.
|t Fourier Series.
|d Washington : Mathematical Association of America, ©2014
|z 9780883857403
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