Abstract
In this chapter we introduce the p-trigonometric functions, for 1\(< p < \infty, \) and establish their fundamental properties. These functions generalise the familiar trigonometric functions, coincide with them when p = 2, and otherwise have important similarities to and differences from their classical counterparts. As will be shown later, they play an important part in both the theory of the p-Laplacian and that of the Hardy operator. Particular attention is paid to the basis properties of the analogues of the sine functions in the context of Lebesgue spaces.
Keywords
- Trigonometric Function
- Lebesgue Space
- Classical Counterpart
- Hardy Operator
- Incomplete Beta Function
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© 2011 Springer-Verlag Berlin Heidelberg
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Lang, J., Edmunds, D. (2011). Trigonometric Generalisations. In: Eigenvalues, Embeddings and Generalised Trigonometric Functions. Lecture Notes in Mathematics(), vol 2016. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18429-1_2
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DOI: https://doi.org/10.1007/978-3-642-18429-1_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18267-9
Online ISBN: 978-3-642-18429-1
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