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A note on interpolation of a certain class of functions. (English) Zbl 0811.41007
Summary: The approximate functions for certain periodic functions of several variables are constructed by means of the number-theoretic method.

MSC:
41A05 Interpolation in approximation theory
11K99 Probabilistic theory: distribution modulo \(1\); metric theory of algorithms
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References:
[1] Hua Loo-Keng and Wang Yuan. Applications of Number Theory to Numerical Analysis. Springer-Verlag, New York, 1981. · Zbl 0451.10001
[2] Korobov, N.M. Number Theoretic Methods in Approximate Analysis. Fizmatigiz, Moscow, 1963. · Zbl 0115.11703
[3] Rjabenkii, V.S. Tables and Interpolation of a Certain Class of Functions.Dokl. Akad. Nauk SSSR, 1960, 131 (5): 1025–1027.
[4] Temljakov, V.N. On Reconstruction of Multivariate Periodic Functions Based on Their Values at the Knots of Number-theoretic Nets.Analysis Math., 1986, 12 (4): 287–305. · Zbl 0621.41004 · doi:10.1007/BF01909367
[5] Wang Yuan. A Note on Interpolation of a Certain Class of Function.Sci. Sin., 1960, 10 (6): 632–636. · Zbl 0202.44004
[6] Zhu Yaochen. On Some Multi-dimensional Quadrature Formulas with Number-theoretic Nets.Acta Mathematicae Applicatae Sinica, 1993, 9 (4): 333–347. · Zbl 0803.11043 · doi:10.1007/BF02005922
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