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Problems and remarks on Chapter 1
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absolutely continuous absolutely convergent Alexits An(dx analytic bounded variation Br(dx Cauchy's integral formula Chebyshev polynomials coefficients condition consequence D(dfi denote dx(t dx(x equal estimate finite interval fixed Fourier series Freud function f(x furthermore gonal holds uniformly hypotheses of Theorem implies inequality infer integral interpolation Jacobi polynomials Kn(dx Legendre polynomials Lemma Let f(x m-distribution dx m-distribution function momentum problem nomials non-decreasing non-negative obtain open unit circle orthogonal expansion orthogonal polynomials partial sums pn(dx pn(dx;x pn(x point x0 polynomial of degree proof of Theorem proved our statement quadrature formula radial limit value real numbers relation Remark Riesz right-hand side sequence of polynomials shows the validity Stieltjes Stieltjes integrable sufficiently large Suppose sv(dx Szego Theorem 7.4 tion uniform convergence uniformly bounded uniformly satisfied uniformly with respect vanishes weight function whence zeros Zygmund