Approximation in Müntz Spaces MΛ,p of Lp Functions for 1 < p < ∞ and Bases
Müntz spaces satisfying the Müntz and gap conditions are considered. A Fourier approximation of functions in the Müntz spaces MΛ,p of Lp functions is studied, where 1 < p < ∞. It is proven that up to an isomorphism and a change of variables, these spaces are contained in Weil–Nagy’s cl...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-01-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/5/1/10 |
| _version_ | 1818950427033468928 |
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| author | Sergey V. Ludkowski |
| author_facet | Sergey V. Ludkowski |
| author_sort | Sergey V. Ludkowski |
| collection | DOAJ |
| description | Müntz spaces satisfying the Müntz and gap conditions are considered. A Fourier approximation of functions in the Müntz spaces MΛ,p of Lp functions is studied, where 1 < p < ∞. It is proven that up to an isomorphism and a change of variables, these spaces are contained in Weil–Nagy’s class. Moreover, the existence of Schauder bases in the Müntz spaces MΛ,p is investigated. |
| first_indexed | 2024-12-20T09:18:25Z |
| format | Article |
| id | doaj.art-fb683d5279c14b4fac7e65d23a134a81 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-20T09:18:25Z |
| publishDate | 2017-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fb683d5279c14b4fac7e65d23a134a812022-12-21T19:45:21ZengMDPI AGMathematics2227-73902017-01-01511010.3390/math5010010math5010010Approximation in Müntz Spaces MΛ,p of Lp Functions for 1 < p < ∞ and BasesSergey V. Ludkowski0Department of Applied Mathematics, Moscow State Technological University MIREA, Av. Vernadsky 78, Moscow 119454, RussiaMüntz spaces satisfying the Müntz and gap conditions are considered. A Fourier approximation of functions in the Müntz spaces MΛ,p of Lp functions is studied, where 1 < p < ∞. It is proven that up to an isomorphism and a change of variables, these spaces are contained in Weil–Nagy’s class. Moreover, the existence of Schauder bases in the Müntz spaces MΛ,p is investigated.http://www.mdpi.com/2227-7390/5/1/10Banach spaceMüntz spaceisomorphismSchauder basisFourier series |
| spellingShingle | Sergey V. Ludkowski Approximation in Müntz Spaces MΛ,p of Lp Functions for 1 < p < ∞ and Bases Mathematics Banach space Müntz space isomorphism Schauder basis Fourier series |
| title | Approximation in Müntz Spaces MΛ,p of Lp Functions for 1 < p < ∞ and Bases |
| title_full | Approximation in Müntz Spaces MΛ,p of Lp Functions for 1 < p < ∞ and Bases |
| title_fullStr | Approximation in Müntz Spaces MΛ,p of Lp Functions for 1 < p < ∞ and Bases |
| title_full_unstemmed | Approximation in Müntz Spaces MΛ,p of Lp Functions for 1 < p < ∞ and Bases |
| title_short | Approximation in Müntz Spaces MΛ,p of Lp Functions for 1 < p < ∞ and Bases |
| title_sort | approximation in muntz spaces mλ p of lp functions for 1 lt p lt ∞ and bases |
| topic | Banach space Müntz space isomorphism Schauder basis Fourier series |
| url | http://www.mdpi.com/2227-7390/5/1/10 |
| work_keys_str_mv | AT sergeyvludkowski approximationinmuntzspacesmlpoflpfunctionsfor1ltpltandbases |