Abstract
In Section 2.5 we defined the sum function associated to a given family of functions f0, fl,... defined on the same set. However, in practice sum functions frequently appear in a different way: a certain class of functions is given, and we want to find “simple functions” f0, fl,... such that each function f in the class has an expansion
for some coefficients a n . We note that this idea is similar to what we have seen in the context of power series and Fourier series: these cases correspond to the functions f n being polynomials or trigonometric functions, respectively.
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© 2004 Springer Science+Business Media New York
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Christensen, O., Christensen, K.L. (2004). Wavelets and Applications. In: Approximation Theory. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4448-2_4
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DOI: https://doi.org/10.1007/978-0-8176-4448-2_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3600-5
Online ISBN: 978-0-8176-4448-2
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