多项式和多项式不等式

出版时间：2011-7-1  出版社：世界图书出版公司  作者：Peter Borwein Tamas Erdelyi  页数：480  
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内容概要

　　《多项式和多项式不等式(英文版)》是springer数学研究生教材（gtm）第161卷，主要介绍多项式和有理函数，重点论述代数多项式和三角多项式的特性，同时也介绍了多项式几何、正交多项式、切比雪夫和马可夫系、müntz系和müntz-type型稠密性定理，以及不等式用于多项式和有理函数等理论。其中有些内容较同类图书更加全面。目次：导论和基本特性；特殊多项式；切比雪夫和笛卡儿系；稠密性问题；基本不等式；müntz空间中的不等式；有理函数空间中的不等式。
　　读者对象：数学及相关专业研究生和科研人员。

书籍目录

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