The degree of coconvex polynomial approximation

Authors:
K. Kopotun, D. Leviatan and I. A. Shevchuk

Journal:
Proc. Amer. Math. Soc. **127** (1999), 409-415

MSC (1991):
Primary 41A10, 41A17, 41A25, 41A29

MathSciNet review:
1459130

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Abstract | References | Similar Articles | Additional Information

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 Ditzian-Totik 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/S0002-9939-99-04452-4

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 N00014-91-1076 and by DoD grant N00014-94-1-1163.

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