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

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