Diameters of Sets in Function Spaces and the Theory of Best Approximations

CONTENTS Introduction § 1. Survey of results which relate to special classes of functions § 2. A theorem on the diameters of a sphere § 3. Estimates from below of the diameters of the classes , , , , § 4. Best approximations by trigonometric sums to the classes , , § 5. Investigation of the classes § 6. An elementary estimate from below of the diameters and some of its applications § 7. Two examples References