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Fourier Series

In: An Introduction to Modern Analysis

Author

Listed:
  • Vicente Montesinos

    (Universitat Politècnica de València, Departamento de Matemática Aplicada Instituto de Matemática Pura y Aplicada)

  • Peter Zizler

    (Mount Royal University, Department of Mathematics, Physics and Engineering)

  • Václav Zizler

    (University of Alberta, Department of Mathematical and Statistical Sciences)

Abstract

The goal of Fourier analysis—a theory that bears the name of the French mathematician and physicist Joseph Fourier Fourier, J. , who initiated the systematic approach to it in order to explain the analytic theory of heat— is to represent functions f defined on ${\mathbb R}$ as the sum of a series whose terms are simple trigonometric functions, i.e., the nowadays called Fourier series of $f$ Fourier series , a series of the form $\frac{a_0}{2}+\sum_{n=1}^{\infty}(a_n\cos nx+b_n\sin nx)$ . This aim may look difficult to achieve, since f is not, in general, $2\pi$ -periodic, while trigonometric functions are. This is not a big problem if f is supposed to be defined on a closed and bounded interval.

Suggested Citation

  • Vicente Montesinos & Peter Zizler & Václav Zizler, 2015. "Fourier Series," Springer Books, in: An Introduction to Modern Analysis, edition 127, chapter 9, pages 455-486, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12481-0_9
    DOI: 10.1007/978-3-319-12481-0_9
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