Approximation characteristics of the isotropic Nikol’skii-Besov functional classes - Yanchenko, S.Ya.; Radchenko, O.Ya. (Carpathian Mathematical Publications, 2021)
In the paper, we investigates the isotropic Nikol'skii-Besov classes B^r_p,θ(R^d) of non-periodic functions of several variables, which for d = 1 are identical to the classes of functions with a dominant mixed smoothness S^r_p,θB(R). We establish the exact-order estimates for the approximation of functions from these classes B^r_p,θ(R^d) in the metric of the Lebesgue space L_q(R^d), by entire functions of exponential type with some restrictions for their spectrum in the case 1 p q ∞, (p,q) eq {(1,1), (∞, ∞)}, d≥ 1. In the case 2<p=q<∞, d=1, the established estimate is also new for the classes S^r_p,θB(R).