Fourier Series

Vicente Montesinos (), Peter Zizler () and Václav Zizler ()
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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

Chapter 9 in An Introduction to Modern Analysis, 2015, pp 455-486 from Springer

Abstract: 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.

Keywords: Fourier Series; Periodic Function; Pointwise Convergence; Orthonormal System; Dirichlet Kernel (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-12481-0_9

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