The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates
Given μ>-1/2 and c∈I=]0,∞[, let the space Cμ,c (respectively, Cμ) consist of all those continuous functions u on ]0,c] (respectively, I) such that the limit limz→0+z-μ-1/2u(z) exists and is finite; Cμ,c is endowed with the uniform norm uμ,∞,c=supz∈[0,c]z-μ-1/2u(z) (u∈Cμ,c). Assume ϕ∈Cμ defines...
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/1845491 |
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| author | Isabel Marrero |
| author_facet | Isabel Marrero |
| author_sort | Isabel Marrero |
| collection | DOAJ |
| description | Given μ>-1/2 and c∈I=]0,∞[, let the space Cμ,c (respectively, Cμ) consist of all those continuous functions u on ]0,c] (respectively, I) such that the limit limz→0+z-μ-1/2u(z) exists and is finite; Cμ,c is endowed with the uniform norm uμ,∞,c=supz∈[0,c]z-μ-1/2u(z) (u∈Cμ,c). Assume ϕ∈Cμ defines an absolutely regular Hankel-transformable distribution. Then, the linear span of dilates and Hankel translates of ϕ is dense in Cμ,c for all c∈I if, and only if, ϕ∉πμ, where πμ=span{t2n+μ+1/2:n∈Z+}. |
| format | Article |
| id | doaj-art-031019ee1d67474e9e57e26fc6b6d261 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-031019ee1d67474e9e57e26fc6b6d2612025-02-03T06:01:23ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/18454911845491The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel TranslatesIsabel Marrero0Departamento de Análisis Matemático, Universidad de La Laguna, Aptdo. 456, 38200 La Laguna, Tenerife, SpainGiven μ>-1/2 and c∈I=]0,∞[, let the space Cμ,c (respectively, Cμ) consist of all those continuous functions u on ]0,c] (respectively, I) such that the limit limz→0+z-μ-1/2u(z) exists and is finite; Cμ,c is endowed with the uniform norm uμ,∞,c=supz∈[0,c]z-μ-1/2u(z) (u∈Cμ,c). Assume ϕ∈Cμ defines an absolutely regular Hankel-transformable distribution. Then, the linear span of dilates and Hankel translates of ϕ is dense in Cμ,c for all c∈I if, and only if, ϕ∉πμ, where πμ=span{t2n+μ+1/2:n∈Z+}.http://dx.doi.org/10.1155/2019/1845491 |
| spellingShingle | Isabel Marrero The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates Journal of Function Spaces |
| title | The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates |
| title_full | The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates |
| title_fullStr | The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates |
| title_full_unstemmed | The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates |
| title_short | The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates |
| title_sort | role of nonpolynomiality in uniform approximation by rbf networks of hankel translates |
| url | http://dx.doi.org/10.1155/2019/1845491 |
| work_keys_str_mv | AT isabelmarrero theroleofnonpolynomialityinuniformapproximationbyrbfnetworksofhankeltranslates AT isabelmarrero roleofnonpolynomialityinuniformapproximationbyrbfnetworksofhankeltranslates |