The degree of coconvex polynomial approximation
Authors:
K. Kopotun, D. Leviatan and I. A. Shevchuk
Journal:
Proc. Amer. Math. Soc. 127 (1999), 409415
MSC (1991):
Primary 41A10, 41A17, 41A25, 41A29
MathSciNet review:
1459130
Fulltext PDF Free Access
Abstract 
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Abstract: Let change its convexity finitely many times in the interval, say times, at . We estimate the degree of approximation of by polynomials of degree , which change convexity exactly at the points . We show that provided is sufficiently large, depending on the location of the points , the rate of approximation is estimated by the third DitzianTotik modulus of smoothness of multiplied by a constant , which depends only on .
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Additional Information
K. Kopotun
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Address at time of publication:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email:
kkopotun@math.vanderbilt.edu
D. Leviatan
Affiliation:
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel and Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email:
leviatan@math.tau.ac.il
I. A. Shevchuk
Affiliation:
Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv 252601, Ukraine
Email:
shevchuk@dad.imath.kiev.ua
DOI:
http://dx.doi.org/10.1090/S0002993999044524
PII:
S 00029939(99)044524
Keywords:
Coconvex polynomial approximation,
Jackson estimates
Received by editor(s):
May 9, 1996
Received by editor(s) in revised form:
April 1, 1997
Additional Notes:
The first author acknowledges partial support by the Izaak Walton Killam Memorial Scholarship.
The second author acknowledges partial support by ONR grant N00014911076 and by DoD grant N000149411163.
The third author was partially supported by the State Fund for Fundamental Research of Ukraine.
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1999
American Mathematical Society
