Open AccessOn the best polynomial approximation of $2\pi$-periodic functions in the $L_2$ space
Author(s) -
С. Б. Вакарчук
Publication year - 2015
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241503
Subject(s) - pi , smoothness , mathematics , polynomial , combinatorics , order (exchange) , space (punctuation) , type (biology) , mathematical analysis , pure mathematics , geometry , ecology , linguistics , philosophy , finance , economics , biology
On the classes $L^r_2$, where $r\in {\mathbb{Z}}_+$, exact constants of Jackson type inequalities have been obtained for the characteristics of smoothness ${\Delta}_k (f)$, $k\in \mathbb{N}$, which are defined by the averaged $k$-th order finite differences of functions $f\in L_2$.