Pointwise convergence of wavelet expansion of \({{\mathcal K}_M^r}'(R)\). (English) Zbl 0988.46034

Sohn, Byung Keun; Pahk, Dae Hyeon

Bull. Korean Math. Soc. 38, No. 1, 81-91 (2001).

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

MSC:

46F20	Distributions and ultradistributions as boundary values of analytic functions
42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
41A15	Spline approximation
46F10	Operations with distributions and generalized functions

Keywords:

wavelet; generalized tempered distribution