多項(xiàng)式和多項(xiàng)式不等式

內(nèi)容概要

　　《多項(xiàng)式和多項(xiàng)式不等式(英文版)》是springer數(shù)學(xué)研究生教材（gtm）第161卷，主要介紹多項(xiàng)式和有理函數(shù)，重點(diǎn)論述代數(shù)多項(xiàng)式和三角多項(xiàng)式的特性，同時(shí)也介紹了多項(xiàng)式幾何、正交多項(xiàng)式、切比雪夫和馬可夫系、müntz系和müntz-type型稠密性定理，以及不等式用于多項(xiàng)式和有理函數(shù)等理論。其中有些內(nèi)容較同類圖書更加全面。目次：導(dǎo)論和基本特性；特殊多項(xiàng)式；切比雪夫和笛卡兒系；稠密性問題；基本不等式；müntz空間中的不等式；有理函數(shù)空間中的不等式。
　　讀者對(duì)象：數(shù)學(xué)及相關(guān)專業(yè)研究生和科研人員。

書籍目錄

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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