A Complete Asymptotic Expansion for the Quasi-interpolants of Gauß–Weierstraß Operators

We derive the complete asymptotic expansion for the quasi-interpolants of Gauß–Weierstraß operators W n and their left quasi-interpolants W n r with explicit representation of the coefficients. The results apply to all locally integrable real functions f on R satisfying the growth condition f t = O...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2018-08, Vol.15 (4), p.1-10, Article 156
Main Authors: Abel, Ulrich, Agratini, Octavian, Păltănea, Radu
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic series
Mathematics
Mathematics and Statistics
Operators
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Summary:We derive the complete asymptotic expansion for the quasi-interpolants of Gauß–Weierstraß operators W n and their left quasi-interpolants W n r with explicit representation of the coefficients. The results apply to all locally integrable real functions f on R satisfying the growth condition f t = O e c t 2 as t → + ∞ , for some c > 0 . All expansions are shown to be valid also for simultaneous approximation.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-018-1195-8