# Elementary solutions of the Bernstein problem on two intervals

Pausinger F. 2012. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 8(1), 63–78.

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Abstract

First we note that the best polynomial approximation to vertical bar x vertical bar on the set, which consists of an interval on the positive half-axis and a point on the negative half-axis, can be given by means of the classical Chebyshev polynomials. Then we explore the cases when a solution of the related problem on two intervals can be given in elementary functions.

Publishing Year

Date Published

2012-01-01

Journal Title

Journal of Mathematical Physics, Analysis, Geometry

Acknowledgement

This work is supported by the Austrian Science Fund (FWF), Project P22025-N18.

Volume

8

Issue

1

Page

63-78

ISSN

IST-REx-ID

### Cite this

Pausinger F. Elementary solutions of the Bernstein problem on two intervals.

*Journal of Mathematical Physics, Analysis, Geometry*. 2012;8(1):63-78.Pausinger, F. (2012). Elementary solutions of the Bernstein problem on two intervals.

*Journal of Mathematical Physics, Analysis, Geometry*. B. Verkin Institute for Low Temperature Physics and Engineering.Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.”

*Journal of Mathematical Physics, Analysis, Geometry*. B. Verkin Institute for Low Temperature Physics and Engineering, 2012.F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals,”

*Journal of Mathematical Physics, Analysis, Geometry*, vol. 8, no. 1. B. Verkin Institute for Low Temperature Physics and Engineering, pp. 63–78, 2012.Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.”

*Journal of Mathematical Physics, Analysis, Geometry*, vol. 8, no. 1, B. Verkin Institute for Low Temperature Physics and Engineering, 2012, pp. 63–78.**All files available under the following license(s):**

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