Turan Extremum Problem for Periodic Function with Small Support

D. V. Gorbachev; A. S. Manoshina

Turan Extremum Problem for Periodic Function with Small Support

经典分析与常微分方程 2007-05-23 v1 数论

作者: D. V. Gorbachev , A. S. Manoshina

摘要

We consider an extremum problem posed by Turan. The aim of this problem is to find a maximum mean value of 1-periodic continuous even function such that sum of Fourier coefficient modules for this function is equal to 1 and support of this function lies in $[-h,h]$ , $0<h\le 1/2$ . We show that this extremum problem for rational $h=p/q$ is equivalent two finite-dimensional linear programming problems. Here there are exact results for rational $h=2/q$ , $h=p/(2p+1)$ , $h=3/q$ , and asymptotic equalities.

关键词

optimization and approximation theory function spaces and inequalities

引用

@article{arxiv.math/0211291,
  title  = {Turan Extremum Problem for Periodic Function with Small Support},
  author = {D. V. Gorbachev and A. S. Manoshina},
  journal= {arXiv preprint arXiv:math/0211291},
  year   = {2007}
}

备注

8 pages

Turan Extremum Problem for Periodic Function with Small Support

摘要

关键词

引用

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