preface chapter 1 introduction and basic properties 1.1 polynomials and rational functions 1.2 the fundamental theorem of algebra 1.3 zeros of the derivative chapter 2 some special polynomials 2.1 chebyshev polynomials 2.2 orthogonal functions 2.3 orthogonal polynomials 2.4 polynomials with nonnegative coefficients chapter 3 chebyshev and descartes systems 3.1 chebyshev systems 3.2 descartes systems 3.3 chebyshev polynomials in chebyshev spaces 3.4 miintz-legendre polynomials 3.5 chebyshev polynomials in rational spaces chapter 4 denseness questions 4.1 variations on the weierstrass theorem 4.2 miintz's theorem 4.3 unbounded bernstein inequalities 4.4 miintz rationals chapter 5 basic inequalities 5.1 classical polynomial inequalities 5.2 markov's inequality for higher derivatives 5.3 inequalities for norms of factors chapter 6 inequalities in muntz spaces 6.1 inequalities in mfintz spaces 6.2 nondense miintz spaces chapter 7 inequalities for rational function spaces 7.1 inequalities for rational function spaces 7.2 inequalities for logarithmic derivatives appendix a1 algorithms and computational concerns appendix a2 orthogonality and irrationality appendix a3 an interpolation theorem appendix a4 inequalities for generalized polynomials in lp appendix a5 inequalities for polynomials with constraints bibliography notation index
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