Generalized Jacobi–Weierstrass operators and Jacobi expansions

Abstract

Abstract We present a realization for some K-functionals associated with Jacobi expansions in terms of generalized Jacobi–Weierstrass operators. Fractional powers of the operators as well as results concerning simultaneous approximation and Nikolskii–Stechkin type inequalities are also considered.

Keywords

• Jacobi–Weierstrass operators
• Abel–Cartwright means
• Realization of K-functionals
• Semi-groups of operators
• Fractional powers
• Nikolskii–Stechkin type inequality