Recovering Pointwise Values of Discontinuous Data within Spectral Accuracy
David J. Gottlieb, Eitan Tadmor · Birkhäuser Boston eBooks · 1985
Let f(x) be a bounded 2π-periodic function whose Fourier coefficients are given by 1.1 $${\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{f}}(k) = {{\frac{1}{2}}_{\pi }}\int\limits_{{ - \pi }}^{\pi } {f(y){{e}^{{ - ik \bullet y}}}dy, - \infty }}\;{\text{1}}{\text{.}} $$ Here and below, CS stands for (possibly different) generic constant bounds, and ||f||(S) denotes the largest maximum norm of f and its first s derivatives, the maximum taken over the whole domain.