General properties of Fourier series for piecewise continuously differentiable functions are worked out. This includes symmetry properties, amplitude modulation, derivatives and integrals of Fourier series, asymptotic decay of Fourier coefficients, spectrum, and the Parseval equation. An example of an everywhere convergent trigonometric series is given that cannot be the Fourier series of a classical function. Further examples and exercises on the contents complement the chapter.

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Calculating with Fourier Series

  • Rolf Brigola

摘要

General properties of Fourier series for piecewise continuously differentiable functions are worked out. This includes symmetry properties, amplitude modulation, derivatives and integrals of Fourier series, asymptotic decay of Fourier coefficients, spectrum, and the Parseval equation. An example of an everywhere convergent trigonometric series is given that cannot be the Fourier series of a classical function. Further examples and exercises on the contents complement the chapter.