Chebyshev and equilibrium measure vs. Bernstein and Lebesgue measure
Chebyshev and equilibrium measure vs. Bernstein and Lebesgue measure
We show that Bernstein polynomials are related to the Lebesgue measure on [0, 1] in a manner similar as Chebyshev polynomials are related to the equilibrium measure of [--1, 1]. We also show that Pell's polynomial equation satisfied by Chebyshev polynomials, provides a partition of unity of [--1, 1], the …