Karlin S., Studden W.J. Tchebycheff systems: with applications in analysis and statistics

John Wiley & Sons, 1966. — 586 p.A Tchebycheff system plays an important role (sometimes indirectly) in numerous domains of mathematical analysis, notably (a) the theory of approximations, where the chief applications are to interpolation methods, quadrature formulas, and smoothing of data; (b) boundary value problems and problems involving oscillation properties of zeros in solutions of «nth-order differential equations; and (c) the theory of inequalities, especially in its statistical applications. Other related areas are convexity, numerical analysis, summability, transform operators, and variational problems involving classes of polynomials.