On rational approximation of functions in rearrangement invariant spaces

Abstract

Some direct theorems for polynomial and rational approximation of functions in the complex plane are proved.

Approximation in weighted rearrangement invariant Smirnov spaces

“…The problems of approximation theory for weighted rearrangement invariant spaces are studied in [17], [19], [23] and [51]. In this work, we prove a direct theorem of approximation theory in weighted rearrangement invariant Smirnov spaces.…”

On approximation of functions by rational functions in weighted generalized grand Smirnov classes

“…In this study the approximation problems of the functions by Faber-Laurent rational functions in the weighted generalized grand Smirnov classes E p),θ (G, ω), θ > 0, defined in the doubly connected domains with the regular boundaries are studied. Similar problems in the different spaces were investigated by several authors (see for example, [1][2][3][4][5][14][15][16][17][18][19][20][21][22][23]25,[27][28][29][30][31][32]38,39]).…”

Approximation by p-Faber -Laurent rational functions in doubly-connected domain

“…The problems of approximation of the functions in the non-weighted and weighted Smirnov classes were investigated in [1, 2, 5, 9-13, 16, 17, 22]. Similar problems in the different spaces defined on the continuums of the complex plane were investigated by several authors (see for example, [3,8,14,15,[18][19][20][21][25][26][27]). We remark, that when Γ is a closed regular Jordan curve, the approximation properties of the p−Faber-Laurent rational series expansions in the ω− Lebesgue spaces L p (Γ, ω) have been investigated by Israfilov [16].…”