Abstract
The paper aims at a generalization of the Gauss–Weierstrass integral introduced by Eugeniusz Wachnicki two decades ago. It is intimately connected to a generalization of the heat equation. The main result is an asymptotic expansion for the operators when applied to a function belonging to a rather large class. An essential auxiliary result is a localization theorem which is interesting in itself.
Authors
Octavian Agratini
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Keywords
Gauss–Weierstrass operator; Bessel function; Kummer function; Asymptotic expansion; Degree of approximation
Paper coordinates
U. Abel and O. Agratini, On Wachnicki’s Generalization of the Gauss-Weierstrass Integral, In: Candela, A.M., Cappelletti Montano, M., Mangino, E. (eds) Recent advances in Mathematical Analysis. Trends in Mathematics, Birkhäuser, Cham.,
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Journal
Recent Advances in Mathematical Analysis
Publisher Name
Birkhäuser, Cham
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