Bulletin of the
Korean Mathematical Society BKMS

For piecewise continuous function $f$ with discontinuity at point $\alpha$, the wavelet expansion of $f$ at $\alpha$ converges different value according to the position of $\alpha$. This property is quite different from that of the Fourier series. In this paper this behavior is analysized.

Keywords: scaling function, wavelet, orthogonal system, wavelet expansion

MSC numbers: 40A05, 41A30, 41A58