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On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces

Ashurov, Ravshan (2011) On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces. Pertanika Journal of Science & Technology, 19 (S). pp. 11-14. ISSN 0128-7680; ESSN: 2231-8526

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Abstract

The partial integrals of the N-fold Fourier integrals connected with elliptic polynomials (not necessarily homogeneous; principal part of which has a strictly convex level surface) are considered. It is proved that if a + s > (N – 1)/2 and ap = N then the Riesz means of the nonnegative orders of the N-fold Fourier integrals of continuous finite functions from the Sobolev spaces Wpa(RN) converge uniformly on every compact set, and if a + s > (N – 1)/2 and ap = N, then for any x0∈ RN there exists a continuous finite function from the Sobolev space such, that the corresponding Riesz means of the N-fold Fourier integrals diverge to infinity at x0. AMS 2000 Mathematics Subject Classifications: Primary 42B08; Secondary 42C14

Item Type:Article
Keyword:N-fold fourier integrals; Elliptic polynomials; Continuous functions from the Sobolev spaces; Uniformly convergence
Faculty or Institute:Institute of Advanced Technology
Publisher:Universiti Putra Malaysia Press
ID Code:40412
Deposited By: Noor Syafini Zamani
Deposited On:18 Nov 2015 13:57
Last Modified:18 Nov 2015 13:57

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