Description: In 1807 the French mathematician and physicist Jean Baptiste Joseph Fourier announced his revolutionary theory for the solution of boundary-value problems in partial differential equations. Fourier's landmark technique -- allowing the representation of almost any function of a real variable with a series involving the sines and cosines of integral multiples of the variable -- receives a sophisticated treatment In this classic text. The volume is geared toward mathematicians already familiar with the elements of Lebesgue's theory of integration. Beginning with a brief introduction to some generalities about trigonometrical series, the book proceeds to discussions of the Fourier series in Hilbert space and further properties of trigonometrical Fourier series as well as their convergence and summability, concluding with a detailed look at the applications of previously outlined theorems. This graduate level monograph is ideally suited both for individual and classroom study.

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