Abstract
This chapter explains that many functions are closely approximated by smooth functions, meaning functions whose derivatives of all orders exist. The approximation technology is the convolution, essentially integration against a tall, narrow pulse. Having discussed approximation by convolution, we may freely assume from now on that our functions are smooth.
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© 2016 Springer International Publishing AG
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Shurman, J. (2016). Approximation by Smooth Functions. In: Calculus and Analysis in Euclidean Space. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-49314-5_7
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DOI: https://doi.org/10.1007/978-3-319-49314-5_7
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49312-1
Online ISBN: 978-3-319-49314-5
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