Approximation methods for a class of discrete Wiener-Hopf equations
In this paper, we consider approximation methods for operator equations of the form \[Au + Bu = f,\] where \(A\) is a discrete Wiener-Hopf operator on \(l_p\) (\(1 \leq p \lt \infty\)) which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on per...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2009-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol29/3/art/opuscula_math_2922.pdf |
| _version_ | 1819243643507048448 |
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| author | Michał A. Nowak |
| author_facet | Michał A. Nowak |
| author_sort | Michał A. Nowak |
| collection | DOAJ |
| description | In this paper, we consider approximation methods for operator equations of the form \[Au + Bu = f,\] where \(A\) is a discrete Wiener-Hopf operator on \(l_p\) (\(1 \leq p \lt \infty\)) which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation \(B\) and \(f\) are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces. |
| first_indexed | 2024-12-23T14:58:58Z |
| format | Article |
| id | doaj.art-8af8315caf864e88bb79186a1b415c74 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-23T14:58:58Z |
| publishDate | 2009-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-8af8315caf864e88bb79186a1b415c742022-12-21T17:42:41ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742009-01-01293271288http://dx.doi.org/10.7494/OpMath.2009.29.3.2712922Approximation methods for a class of discrete Wiener-Hopf equationsMichał A. Nowak0AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, PolandIn this paper, we consider approximation methods for operator equations of the form \[Au + Bu = f,\] where \(A\) is a discrete Wiener-Hopf operator on \(l_p\) (\(1 \leq p \lt \infty\)) which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation \(B\) and \(f\) are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.http://www.opuscula.agh.edu.pl/vol29/3/art/opuscula_math_2922.pdfprojection methodsiterative methodsdiscrete Wiener-Hopf equationsToeplitz operators |
| spellingShingle | Michał A. Nowak Approximation methods for a class of discrete Wiener-Hopf equations Opuscula Mathematica projection methods iterative methods discrete Wiener-Hopf equations Toeplitz operators |
| title | Approximation methods for a class of discrete Wiener-Hopf equations |
| title_full | Approximation methods for a class of discrete Wiener-Hopf equations |
| title_fullStr | Approximation methods for a class of discrete Wiener-Hopf equations |
| title_full_unstemmed | Approximation methods for a class of discrete Wiener-Hopf equations |
| title_short | Approximation methods for a class of discrete Wiener-Hopf equations |
| title_sort | approximation methods for a class of discrete wiener hopf equations |
| topic | projection methods iterative methods discrete Wiener-Hopf equations Toeplitz operators |
| url | http://www.opuscula.agh.edu.pl/vol29/3/art/opuscula_math_2922.pdf |
| work_keys_str_mv | AT michałanowak approximationmethodsforaclassofdiscretewienerhopfequations |