Chebyshev Splines And Kolmogorov Inequalities

This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity w. In particular an extensive account is given of structural limiting and extremal properties of perfect wsplines generalizing standard polynomial perfect splines in the theory of Sobolev classes. In this context special attention is paid to the qualitative description of Chebyshev wsplines and wpolynomials associated with the Kolmogorov problem of nwidth