Syllabus
The Kolmogorov theorem and its consequences, the Fenchel theorem, the Caratheodory theorem, the Rivlin-Shapiro theorem, the Chebyshev alternation theorem, the de la Vallee-Poussin theorem, Markov systems, Chebyshev polynomials, strong unicity of the best approximation, Lipschitz spaces, Marchaud inequality, direct and inverse theorems of trigonometric approximation, Jackson-type theorems, saturation classes, approximation of functions by algebraic polynomials.
Annotation
Advanced topics in theory of approximations.