Moduli of Smoothness and Approximation on the Unit Sphere and the Unit Ball

Details Moduli of Smoothness and Approximation on the Unit Sphere and the Unit Ball Moduli of Smoothness and Approximation on the Unit Sphere and the Unit Ball

2009-07-28

arxiv.org/abs/0907.4968v2

Advances in Mathematics, 224 (2010), 1233- 1310

Mathematics

Classical Analysis and ODEs

63 pages, to appear in Advances in Math

Scientific paper

A new modulus of smoothness based on the Euler angles is introduced on the unit sphere and is shown to satisfy all the usual characteristic properties of moduli of smoothness, including direct and inverse theorem for the best approximation by polynomials and its equivalence to a $K$-functional, defined via partial derivatives in Euler angles. The set of results on the moduli on the sphere serves as a basis for defining new moduli of smoothness and their corresponding $K$-functionals on the unit ball, which are used to characterize the best approximation by polynomials on the ball.

Affiliated with

Also associated with

No associations

Rating

Moduli of Smoothness and Approximation on the Unit Sphere and the Unit Ball does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Moduli of Smoothness and Approximation on the Unit Sphere and the Unit Ball, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Moduli of Smoothness and Approximation on the Unit Sphere and the Unit Ball will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-682444