Summability of a Tchebysheff system of functions
We consider a special type of Tchebysheff systems of functions {ui(⋅)}in=0 and {Vi(⋅)}in=0 defined on the intervals (0, 1] and [1,+∞), respectively, such that ui(t)=tα0∫t1t1α1∫t11t2α2…∫ti−11tiαidtidti−1…dt1 and ui(t)=tβ0∫1tt1β1∫1t1t2β2…∫1ti−1tiβidtidti−1…dt1. We find necessary and sufficient conditi...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/405313 |
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| author | Z. T. Abdikalikova A. A. Kalybay |
| author_facet | Z. T. Abdikalikova A. A. Kalybay |
| author_sort | Z. T. Abdikalikova |
| collection | DOAJ |
| description | We consider a special type of Tchebysheff systems of functions {ui(⋅)}in=0 and {Vi(⋅)}in=0 defined on the intervals (0, 1] and [1,+∞), respectively, such that ui(t)=tα0∫t1t1α1∫t11t2α2…∫ti−11tiαidtidti−1…dt1 and ui(t)=tβ0∫1tt1β1∫1t1t2β2…∫1ti−1tiβidtidti−1…dt1. We find necessary and sufficient conditions under which functions from the investigated systems belong to the corresponding Lebesgue spaces Lp(0, 1) and Lp(1,+∞). In order to prove the main results we obtain lower and upper estimates of these functions that are of independent interest. |
| format | Article |
| id | doaj-art-7de1b6015de54beeaeec1e3e799c06e9 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-7de1b6015de54beeaeec1e3e799c06e92025-08-20T03:35:24ZengWileyJournal of Function Spaces and Applications0972-68022010-01-01818710210.1155/2010/405313Summability of a Tchebysheff system of functionsZ. T. Abdikalikova0A. A. Kalybay1L.N. Gumilyev Eurasian National University, Munaytpasov st., 5, 010008 Astana, KazakhstanKazakhstan Institute of Management, Economics and Strategic Research, Abai ave., 4, 050010 Almaty, KazakhstanWe consider a special type of Tchebysheff systems of functions {ui(⋅)}in=0 and {Vi(⋅)}in=0 defined on the intervals (0, 1] and [1,+∞), respectively, such that ui(t)=tα0∫t1t1α1∫t11t2α2…∫ti−11tiαidtidti−1…dt1 and ui(t)=tβ0∫1tt1β1∫1t1t2β2…∫1ti−1tiβidtidti−1…dt1. We find necessary and sufficient conditions under which functions from the investigated systems belong to the corresponding Lebesgue spaces Lp(0, 1) and Lp(1,+∞). In order to prove the main results we obtain lower and upper estimates of these functions that are of independent interest.http://dx.doi.org/10.1155/2010/405313 |
| spellingShingle | Z. T. Abdikalikova A. A. Kalybay Summability of a Tchebysheff system of functions Journal of Function Spaces and Applications |
| title | Summability of a Tchebysheff system of functions |
| title_full | Summability of a Tchebysheff system of functions |
| title_fullStr | Summability of a Tchebysheff system of functions |
| title_full_unstemmed | Summability of a Tchebysheff system of functions |
| title_short | Summability of a Tchebysheff system of functions |
| title_sort | summability of a tchebysheff system of functions |
| url | http://dx.doi.org/10.1155/2010/405313 |
| work_keys_str_mv | AT ztabdikalikova summabilityofatchebysheffsystemoffunctions AT aakalybay summabilityofatchebysheffsystemoffunctions |