On the Rate of a.e. Convergence by Convolution Type Means
The talk is based on joint work with Walter Trebels (TU Darmstadt). K.I. Oskolkov 1977 raised the problem, how the norm-smoothness of f(x) entails a certain rate of a.e. convergence of an approximation process Ttf(x) towards f(x) for t → 0+ . The purpose of this talk is to demonstrate nearly optimal results concerning the rate of almost everywhere convergence of the Gauss-Weierstrass, Abel-Poisson, and Bochner-Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov space Bs p,p, 1 < p < ∞, 0 < s < 1, then Tmtf(x) − f(x) = ox(ts) a.e. as t → 0 +.
Kennesaw State University Approximation Theory and Harmonic Analysis Workshop
Stokolos, Alexander M..
"On the Rate of a.e. Convergence by Convolution Type Means."
Mathematical Sciences Faculty Presentations.