On the distribution of extremal points of general Chebyshev polynomials
On the distribution of extremal points of general Chebyshev polynomials
For a linear subspace ${\mathcal {U}_n} = {\operatorname {span}}[{\varphi _1}, \ldots ,{\varphi _n}]$ in $C[a,b]$ we introduce general Chebyshev polynomials as solutions of the minimization problem ${\operatorname {min}_{{a_i}}}{\left \| {{\varphi _n} - \sum \nolimits _{i = 1}^{n - 1} {{a_i}{\varphi _i}} } \right \|_C}$. For such a Chebyshev polynomial we …