The paper characterizes when discrete best uniform approximants alternate, proves a Sturm oscillation bound for Jacobi-matrix eigenfunctions, and derives monotone Fourier coefficients for polynomials with removed largest zeros.
Chihara, An Introduction to Orthogonal Polynomials , Gordon and Breach Science Publishers, New York–London–Paris, 1978
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Chebyshev systems and Sturm oscillation theory for discrete polynomials
The paper characterizes when discrete best uniform approximants alternate, proves a Sturm oscillation bound for Jacobi-matrix eigenfunctions, and derives monotone Fourier coefficients for polynomials with removed largest zeros.