# Orthogonality and General Fourier Series

Part of the Texts in Applied Mathematics book series (TAM, volume 29)

## Abstract

In the previous chapters Fourier series have been the main tool for obtaining formal solutions of partial differential equations. The purpose of the present chapter and the two following chapters is to give a more thorough analysis of Fourier series and formal solutions. The Fourier series we have encountered in earlier chapters can be thought of as examples of a more general class of orthogonal series, and many properties of Fourier series can be derived in this general context. In the present chapter we will study Fourier series from this point of view. The next chapter is devoted to convergence properties of Fourier series, while we return to partial differential equations in Chapter 10. There the goal is to show that the formal solutions are in fact rigorous solutions in a strict mathematical sense.

## Keywords

Fourier Series Eigenvalue Problem Orthogonality Property Piecewise Continuous Function Sine Series
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