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Global smoothness preservation by multivariate singular integrals

Published online by Cambridge University Press:  17 April 2009

George A. Anastassiou  and
Sorin G. Gal
George A. Anastassiou
Affiliation:
Department of Mathematical Sciences, The University of Memphis, Memphis TN 38152, United States of America, e-mail: [email protected]
Sorin G. Gal
Affiliation:
Department of Mathematics, University of Oradea, Str. Armatei Romane 5, 3700 Oradea, Romanis, e-mail: [email protected]
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Abstract

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By using various kinds of moduli of smoothness, it is established that the multivariate variants of the well-known singular integrals of Picard, Poisson-Cauchy, Gauss-Weierstrass and their Jackson-type generalisations satisfy the “global smoothness preservation” property. The results are extensions of those proved by the authors for the univariate case.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 489 - 506
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Anastassiou, G.A. and Gal, S.G., ‘General theory of global smoothness preservation by singular integrals, univariate case, J. Comput. Anal. Appl. 1 (1999), 289–317.Google Scholar
[2]Ditzian, Z. and Totik, V., Moduli of smoothness (Springer-Verlag, Berlin, Heidelberg, New York, 1987).CrossRefGoogle Scholar
[3]Timan, A.F., Theory of approximation of functions of a real variable, (in Russian) (Fizmat-giz, Moscow, 1960).Google Scholar