The Markov Moment Problem and Extremal Problems - AMS Book

Explore the advanced mathematical foundations of the Markov Moment Problem and Extremal Problems through this specialized monograph. This text examines a wide range of questions stemming from the classical work of P. L. Chebyshev and A. A. Markov, presenting them from a modern perspective. Readers will find a deep examination of how results and methods from the generalized moment problem connect with the geometry of convex bodies, algebra, and function theory. The book provides a detailed study of the structure of convex and conical hulls of curves and establishes isoperimetric inequalities for convex hulls. Additionally, it constructs a theory for orthogonal and quasiorthogonal polynomials and addresses problems on limiting processes. This volume is an essential resource for mathematicians looking to understand the development and application of these classical theories in contemporary research.