Comparison of approximation properties of generalized polynomials and splines

• Date: 1998
• Main Authors: Babenko, V. F., Kofanov, V. A., Pichugov, S. A., Бабенко, В. Ф., Кофанов, В. А., Пичугов, С. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1998
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4850
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish that, for p ∈ [2, ∞), q = 1 or p = ∞, q ∈ [ 1, 2], the classes W p r of functions of many variables defined by restrictions on the L p-norms of mixed derivatives of order r = (r 1, r 2, ..., r m) are better approximated in the L q-metric by periodic generalized splines than by generali...