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.
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© 1998 Springer-Verlag New York, Inc.
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(1998). Orthogonality and General Fourier Series. In: Introduction to Partial Differential Equations. Texts in Applied Mathematics, vol 29. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22773-3_8
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DOI: https://doi.org/10.1007/978-0-387-22773-3_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98327-1
Online ISBN: 978-0-387-22773-3
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