The Role of Nonpolynomiality in Uniform Approximation by RBF Networks of Hankel Translates. (1st April 2019) - Marrero, Isabel
Abstract : Givenμ > - 1 / 2 andc ∈ I = ] 0, ∞ [, let the spaceC μ, c (respectively, C μ ) consist of all those continuous functionsu on] 0, c ] (respectively, I ) such that the limitlim z → 0 + ⁡ z - μ - 1 / 2 u ( z ) exists and is finite;C μ, c is endowed with the uniform normu μ, ∞, c = sup z ∈ [ 0, c ] ⁡ z - μ - 1 / 2 u ( z )     ( u ∈ C μ, c ) . Assumeϕ ∈ C μ defines an absolutely regular Hankel-transformable distribution. Then, the linear span of dilates and Hankel translates ofϕ is dense inC μ, c for allc ∈ I if, and only if, ϕ ∉ π μ, whereπ μ = s p a n { t 2 n + μ + 1 / 2 : n ∈ Z + } .