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On the regularizations Fourier series of distributions

Rakhimov, Abdumalik A. (2011) On the regularizations Fourier series of distributions. In: 2011 4th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), 19 - 21 April 2011, Kuala Lumpur, Malaysia.

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Abstract

Fourier analysis has many applications in various science and technology. In most problem researchers have to analyze functions (data), which has some singularities. This makes some difficulties in Fourier analysis of singular functional. In these, harmonic analysis in the spaces of distributions can be applied. Recently (see for instance [9]-[11]) interest in spectral expansions of distributions increased and number of research papers were published. Present work it devoted to convergence/summation and regularization of Fourier series of distributions in different topologies. In multidimensional case, convergence essentially depends on methods of summation, i.e. on the definition of partial sums. Even "good" defined partial sums may not supply convergence of Fourier series and in this case, some regularization of the partial sums is required.

Item Type: Conference or Workshop Item (Full Paper)
Additional Information: 6741/24887
Uncontrolled Keywords: Fourier series, summation methods, the Riesz means, distributions, the Sobolev spaces.
Subjects: Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes: Kulliyyah of Engineering > Department of Science
Depositing User: Professor Abdumalik Rakhimov
Date Deposited: 17 Sep 2013 10:27
Last Modified: 17 Sep 2013 10:28
URI: http://irep.iium.edu.my/id/eprint/24887

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