Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4638705 | Journal of Computational and Applied Mathematics | 2015 | 9 Pages |
Abstract
In this paper, we study a special kind of finite Blaschke products called Chebyshev–Blaschke products fn,τfn,τ which can be defined by the Jacobi cosine function cd(u,τ), where τ∈R+iτ∈R+i. We will show that Chebyshev–Blaschke products solve a number of approximation problems, which are related to Zolotarev’s 3rd and 4th problems. More importantly, such a Chebyshev–Blaschke product fn,τfn,τ will be shown to be the finite Blaschke product of degree nn which has the least deviation from zero on [−k(τ),k(τ)], where k(τ)k(τ) is the elliptic modulus. Moreover, certain differential equations for Chebyshev–Blaschke products will be derived.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Tuen Wai Ng, Chiu Yin Tsang,