On a generalized [lambda]-Gauss Weierstrass singular integral

• Autorzy: Aral A.
• Języki publikacji: EN

Abstrakty

EN

In the present note we consider the integral where x należy R_n, s> 0. and Labda1, Labda2,...Labda n are positive numbers with /Labda/ = Labda 1+Labda 2 + ... + Labdan. The integrals Ws(f; x, Alfa) will be called a generalized A—Gauss Weierstrass singular integral. We study some approximation properties of this integral in the nonisotropic exponential weighted space.

Słowa kluczowe

EN

Gauss Weierstrass integral; exponential weighted space

PL

całka Gaussa Weierstrassa

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2005
• Tom: Nr 35
• Strony: 23--33
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Aral A.

• Krikkale University Department of Mathematics, 71450 Yahsihan, Kirikkale - Turkey,

Bibliografia

• [1] A. Aral, On convergence of singular integrals with non-isotropic kernels, Commun Fac. Sci Univ. Ank., Series Al, 50(2001),83-93.
• [2] K. Bogalska, E. Gojtka, M. Gurdek, L. Rempulska, The Picard and the Ciauss-Weierstrass singular integrals of function of two variables, Le Matematiche, LII (1997), 71-85,
• [3] P.L. Butzer, R.J. Nessel, Fourier Analysis and Approximation, Vol 1, Birkhauser, Basel and Acedemic Press, New York 1971.
• [4| V.P. Il'in, O.V. Besov, S.M. Nikolsky, The integral representation of functions and embedding theorems, Nauka, 1975 (in Russian).
• [5] A. Khan, S. Umar, On the order of approximation to a function by generalized Gauss-Weierstrass singular integrals, Commun. Fac. Sci. Univ. Ank., Series Al, 30(1981), 55-62.
• [6] E.M. Stein, Singular Integrals and Differentiabilty Properties of Functions, Princeton University Press, Princeton, New Jersey (1970).