Abstract
In this chapter we shall present elementary results on the convergence of the basic Fourier series, including a proof of completeness of the basic trigonometric systems, and will establish several convenient tools, such as asymptotics of zeros, which are important for practical investigation of these series in the next chapters. Methods of summation and a few explicit examples of q-Fourier series will be also discussed among other things.
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© 2003 Springer Science+Business Media Dordrecht
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Suslov, S.K. (2003). Investigation of Basic Fourier Series. In: An Introduction to Basic Fourier Series. Developments in Mathematics, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3731-8_6
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DOI: https://doi.org/10.1007/978-1-4757-3731-8_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5244-8
Online ISBN: 978-1-4757-3731-8
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