The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates - Isabel Marrero (Journal of Function Spaces)
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+}.