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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
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