This car has excellent brakes that will stop it on a sixpence.
Shortclothes were worn with long stockings.
Now her work dropped on her knee, and her book fell from her hand; she was perpetually seeking excuses for change of place; and the change brought added discomfort.
A central problem in approximation theory is to characterize the best approximation of a function by polynomials, or other classes of simple functions, in terms of the smoothness of the function. In this chapter, we study the characterization of the best approximation by polynomials on the sphere. In the classical setting of one variable, the smoothness of a function on 𝕊¹ is described by the modulus of smoothness, defined by the forward difference.
