In this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

We obtain estimates exact in order for the best approximations and Kolmogorov and trigonometric widths of the classes B p,θ Ω of periodic functions of many variables in the space L q for certain values of the parameters p and q .

No abstract

We obtain exact order estimates for the approximation of the classes B Ω p,θ of periodic functions of many variables in the space Lq by using operators of orthogonal projection and linear operators satisfying certain conditions.