Moduli of smoothness and approximation on the unit sphere and the unit ball
نویسندگان
چکیده
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. It also leads to new moduli of smoothness and K-functionals on the unit ball, which are used to study approximation by polynomials on the ball.
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