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Constructions of univariate and bivariate exponential splines. (English) Zbl 1134.41007

Chuong, N.M. (ed.) et al., Harmonic, wavelet and \(p\)-adic analysis. Based on the summer school, Quy Nhon, Vietnam, June 10–15, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-549-5/hbk). 23-36 (2007).
Univariate and bivariate exponential spline functions with compact supports are constructed by the integral iteration formulas. The properties of exponential splines are explored. Hyperbolic splines are formed as linear combinations of exponential splines and properties are surveyed. Orthonormal exponential splines on small compact supports are constructed in this paper. It is declared that the proposed splines have very nice approximation properties. But the estimations of their approximation accuracy in the functional spaces are not defined. The references on known orthonormal compactly supported functions wavelets and splines [I. Daubechies, Commun. Pure Appl. Math. 41, No. 7, 909–996 (1988; Zbl 0644.42026); V. L. Leontiev and N. C. Lukashanets, Comput. Math. Math. Phys. 39, No. 7, 1116–1126 (1999; Zbl 0970.65012)] are absent.
For the entire collection see [Zbl 1117.42001].

MSC:

41A15 Spline approximation
65D07 Numerical computation using splines
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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