Approximation spaces associated with Legendre differential operators

Abstract

Interpolated scales of approximation spaces and appropriate Bernstein-Jackson inequalities, generated by Legendre differential operators, are considered. Inequalities are applied to spectral approximations of such operators.

Besov-Lorentz-type spaces and best approximations by exponential type vectors

“…From (2) and 3it follows that we have (1) for 1 ≤ p < ∞. The case p = ∞ is a consequence of norm equivalence…”

“…Our goal is to investigate a best approximation problem by subspaces of exponential type entire vectors of an arbitrary unbounded closed linear operator in a Banach space. Thus, this work can be seen as a continuation of [2,3].…”