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Softcover ISBN:  9780821845004 
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Product Code:  MMONO/50.B 
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Softcover ISBN:  9780821845004 
Product Code:  MMONO/50 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470444655 
Product Code:  MMONO/50.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821845004 
eBook ISBN:  9781470444655 
Product Code:  MMONO/50.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 50; 1977; 417 ppMSC: Primary 44; Secondary 42; 52
In this book, an extensive circle of questions originating in the classical work of P. L. Chebyshev and A. A. Markov is considered from the more modern point of view. It is shown how results and methods of the generalized moment problem are interlaced with various questions of the geometry of convex bodies, algebra, and function theory. From this standpoint, the structure of convex and conical hulls of curves is studied in detail and isoperimetric inequalities for convex hulls are established; a theory of orthogonal and quasiorthogonal polynomials is constructed; problems on limiting values of integrals and on least deviating functions (in various metrics) are generalized and solved; problems in approximation theory and interpolation and extrapolation in various function classes (analytic, absolutely monotone, almost periodic, etc.) are solved, as well as certain problems in optimal control of linear objects.
ReadershipGraduate students and research mathematicians interested in analysis.

Table of Contents

Chapters

Preface

Introduction

Convex and orderconvex sets

Čebyšev systems

Canonical representations of generalized moments

The ČebyševMarkov problem

The moment problem on a semiinfinite or infinite interval

The ČebyševMarkov problem with moments in a parallelepiped

Markov’s problem

The ČebyševMarkov problem on a disconnected linear compact set

The abstract $L$problem, duality principle, and some applications


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In this book, an extensive circle of questions originating in the classical work of P. L. Chebyshev and A. A. Markov is considered from the more modern point of view. It is shown how results and methods of the generalized moment problem are interlaced with various questions of the geometry of convex bodies, algebra, and function theory. From this standpoint, the structure of convex and conical hulls of curves is studied in detail and isoperimetric inequalities for convex hulls are established; a theory of orthogonal and quasiorthogonal polynomials is constructed; problems on limiting values of integrals and on least deviating functions (in various metrics) are generalized and solved; problems in approximation theory and interpolation and extrapolation in various function classes (analytic, absolutely monotone, almost periodic, etc.) are solved, as well as certain problems in optimal control of linear objects.
Graduate students and research mathematicians interested in analysis.

Chapters

Preface

Introduction

Convex and orderconvex sets

Čebyšev systems

Canonical representations of generalized moments

The ČebyševMarkov problem

The moment problem on a semiinfinite or infinite interval

The ČebyševMarkov problem with moments in a parallelepiped

Markov’s problem

The ČebyševMarkov problem on a disconnected linear compact set

The abstract $L$problem, duality principle, and some applications