**Translations of Mathematical Monographs**

1977;
417 pp;
Softcover

MSC: Primary 44;
Secondary 42; 52

**Print ISBN: 978-0-8218-4500-4
Product Code: MMONO/50**

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

**Electronic ISBN: 978-1-4704-4465-5
Product Code: MMONO/50.E**

List Price: $129.00

AMS Member Price: $103.20

MAA Member Price: $116.10

# The Markov Moment Problem and Extremal Problems

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*M.G. Kreĭn; A. A. Nudel′man*

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.

#### Readership

Graduate students and research mathematicians interested in analysis.

#### Table of Contents

# Table of Contents

## The Markov Moment Problem and Extremal Problems

- Cover Cover11
- Title page i2
- Contents iii4
- Preface 18
- Introduction 512
- Convex and order-convex sets 714
- Čebyšev systems 3138
- Canonical representations of generalized moments 5764
- The Čebyšev-Markov problem 107114
- The moment problem on a semi-infinite or infinite interval 173180
- The Čebyšev-Markov problem with moments in a parallelepiped 207214
- Markov’s problem 237244
- The Čebyšev-Markov problem on a disconnected linear compact set 287294
- The abstract 𝐿-problem, duality principle, and some applications 331338
- Appendix. Integral representations of analytic functions in certain special classes 389396
- Bibliography 399406
- Subject index 413420
- Back Cover Back Cover1428