Pointwise convergence of wavelet expansion of $\mathcal{K}^r_M ' (R)$

Byung Keun Sohn; Dae Hyeon Pahk

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Bull. Korean Math. Soc. 2001; 38(1): 81-91

Printed March 1, 2001

Pointwise convergence of wavelet expansion of $\mathcal{K}^r_M ' (R)$

Byung Keun Sohn and Dae Hyeon Pahk

Inje University, Yonsei University

Abstract

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Abstract

The expansion of a distribution of ${{\Cal K}_M^r}^\prime (R)$ in terms of regular orthogonal wavelets is considered. The expansion of a distribution of ${{\Cal K}_M^r}^\prime (R)$ is shown to converge pointwise to the value of the distribution where it exists.

Keywords: wavelet, generalized tempered distribution

MSC numbers: 41A15, 46F20