论文信息 - Polynomials of the best uniform approximation to sgn(x) on two intervals - 字舞流文

Polynomials of the best uniform approximation to sgn(x) on two intervals

We describe polynomials of best uniform approximation to sgn(x) on the union of two intervals [−A,−1] ⊂ [1, B] in terms of special conformal mappings. This permits us to find the exact asymptotic behavior of the error in this approximation.

A. Eremenko | P. Yuditskii

[1] G. R. Maclane. Concerning the uniformization of certain Riemann surfaces allied to the inverse-cosine and inverse-gamma surfaces , 1947 .

[2] B. Levin,et al. Distribution of zeros of entire functions , 1964 .

[3] A. Reddy,et al. On the distribution of zeros of entire functions , 1974 .

[4] On Chebychev Approximation on Several Disjoint Intervals , 1980 .

[5] Ben Silver,et al. Elements of the theory of elliptic functions , 1990 .

[6] A. Eremenko,et al. Uniform approximation of sgn x by polynomials and entire functions , 2006, math/0604324.

[7] P. Yuditskii,et al. Asymptotics of the Best Polynomial Approximation of |x|p and of the Best Laurent Polynomial Approximation of sgn(x) on Two Symmetric Intervals , 2009, 0903.3652.