A Complete Asymptotic Expansion for the Quasi-interpolants of Gau-Weierstra Operators

作者：Abel Ulrich^*; Agratini Octavian; Paltanea Radu

来源：Mediterranean Journal of Mathematics, 2018, 15(4): 156.

DOI：10.1007/s00009-018-1195-8

• Approximation by integral operators
• rate of convergence
• degree of approximation
• asymptotic expansions

We derive the complete asymptotic expansion for the quasi-interpolants of Gau-Weierstra operators and their left quasi-interpolants with explicit representation of the coefficients. The results apply to all locally integrable real functions f on satisfying the growth condition as , for some . All expansions are shown to be valid also for simultaneous approximation.

• 出版日期2018-8