MathDB

6

Part of 1982 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1982_6

Source: construct a trigonometric polynomial

1/31/2009
For every positive α \alpha, natural number n n, and at most αn \alpha n points xi x_i, construct a trigonometric polynomial P(x) P(x) of degree at most n n for which P(xi)≤1,  ∫02πP(x)dx=0,   and   max⁡P(x)>cn , P(x_i) \leq 1, \; \int_0^{2 \pi} P(x)dx=0,\ \; \textrm{and}\ \; \max P(x) > cn\ , where the constant c c depends only on α \alpha. G. Halasz
algebrapolynomialintegrationreal analysisreal analysis unsolved