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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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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+}. |
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| ISSN: | 2314-8896 2314-8888 |