TY - JOUR
T1 - On weighted approximation with Jacobi weights
AU - Kopotun, K. A.
AU - Leviatan, D.
AU - Shevchuk, I. A.
N1 - Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/1
Y1 - 2019/1
N2 - We obtain matching direct and inverse theorems for the degree of weighted Lp-approximation by polynomials with the Jacobi weights (1−x)α(1+x)β. Combined, the estimates yield a constructive characterization of various smoothness classes of functions via the degree of their approximation by algebraic polynomials. In addition, we prove Whitney type inequalities which are of independent interest.
AB - We obtain matching direct and inverse theorems for the degree of weighted Lp-approximation by polynomials with the Jacobi weights (1−x)α(1+x)β. Combined, the estimates yield a constructive characterization of various smoothness classes of functions via the degree of their approximation by algebraic polynomials. In addition, we prove Whitney type inequalities which are of independent interest.
KW - Approximation by polynomials in weighted L-norms
KW - Characterization of smoothness classes
KW - Degree of approximation
KW - Direct and inverse theorems
KW - Jacobi weights
KW - Moduli of smoothness
KW - Whitney-type estimates
UR - http://www.scopus.com/inward/record.url?scp=85053751600&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2018.09.003
DO - 10.1016/j.jat.2018.09.003
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AN - SCOPUS:85053751600
SN - 0021-9045
VL - 237
SP - 96
EP - 112
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
ER -