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Wavelet Approximation of Periodic Functions

✍ Scribed by Maria Skopina

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
210 KB
Volume
104
Category
Article
ISSN
0021-9045

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✦ Synopsis

We investigate expansions of periodic functions with respect to wavelet bases. Direct and inverse theorems for wavelet approximation in C and L p norms are proved. For the functions possessing local regularity we study the rate of pointwise convergence of wavelet Fourier series. We also define and investigate the ``discreet wavelet Fourier transform'' (DWFT) for periodic wavelets generated by a compactly supported scaling function. The DWFT has one important advantage for numerical problems compared with the corresponding wavelet Fourier coefficients: while fast computational algorithms for wavelet Fourier coefficients are recursive, DWFTs can be computed by explicit formulas without any recursion and the computation is fast enough.

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