Isabel Marrero

Universal approximation by radial basis function networks of Delsarte translates

We prove that, under certain mild conditions on the kernel function (or activation function), the family of radial basis function neural networks obtained by replacing the usual translation with the Delsarte one, and taking the same smoothing factor in all kernel nodes, has the universal approximation property.

A Hilbert-space approach to Hankel transformable distributions

In this paper we introduce a sequence of Hilbert spaces such that the Hantel integral transformation is a Hilbert-space automorphism of for all r ∊ Z. Topological properties of the spaces are discussed. Finally, Cauchy problems involving the Bessel operator investigated in by using the theory of holomorphic semigroups of linear operators.

Direct form seminorms arising in the theory of interpolation by Hankel translates of a basis function

Certain spaces of functions which arise in the process of interpolation by Hankel translates of a basis function, as developed by the authors elsewhere, are defined with respect to a seminorm which is given in terms of the Hankel transform of each function. This kind of seminorm is called an indirect one. Here we discuss essentially two cases in which the seminorm can be rewritten in direct form, that is, in terms of the function itself rather than its Hankel transform. This is expected to lead to better estimates of the interpolation error.

The Hankel transform of tempered Boehmians via the exchange property

Abstract In this paper the Hankel transformation is defined on a space of tempered Boehmians by means of a simplified construction, patterned after that devised by Atanasiu and Mikusinski for the Fourier transformation, which avoids delta sequences and convergence arguments. In our construction the Hankel convolution plays a central role.

Measures of Noncircularity and Fixed Points of Contractive Multifunctions

In analogy to the Eisenfeld-Lakshmikantham measure of nonconvexity and the Hausdorff measure of noncompactness, we introduce two mutually equivalent measures of noncircularity for Banach spaces satisfying a Cantor type property, and apply them to establish a fixed point theorem of Darbo type for multifunctions. Namely, we prove that every multifunction with closed values, defined on a closed set and contractive with respect to any one of these measures, has the origin as a fixed point.

Hankel- K\{M_{p}\} Spaces

In this paper we introduce the so-called Hankel- K\{M_{p}\} spaces, a family which includes as particular instances many of the spaces of test functions arising in connection with the generalized Hankel transformation. Topological properties of the new spaces are discussed.

Interpolation by Hankel Translates of a Basis Function: Inversion Formulas and Polynomial Bounds

For μ ≥ −1/2, the authors have developed elsewhere a scheme for interpolation by Hankel translates of a basis function Φ in certain spaces of continuous functions Y n (n ∈ ℕ) depending on a weight w. The functions Φ and w are connected through the distributional identity t 4n(h μ′Φ)(t) = 1/w(t), where h μ′ denotes the generalized Hankel transform of order μ. In this paper, we use the projection operators associated with an appropriate direct sum decomposition of the Zemanian space ℋ μ in order to derive explicit representations of the derivatives S μ mΦ and their Hankel transforms, the former ones being valid when m ∈ ℤ + is restricted to a suitable interval for which S μ mΦ is continuous. Here, S μ m denotes the mth iterate of the Bessel differential operator S μ if m ∈ ℕ, while S μ 0 is the identity operator. These formulas, which can be regarded as inverses of generalizations of the equation (h μ′Φ)(t) = 1/t 4n w(t), will allow us to get some polynomial bounds for such derivatives. Corresponding results are obtained for the members of the interpolation space Y n.

Density in Spaces of Interpolation by Hankel Translates of a Basis Function

The function spaces arising in the theory of interpolation by Hankel translates of a basis function, as developed by the authors elsewhere, are defined through a seminorm which is expressed in terms of the Hankel transform of each function and involves a weight . At least two special classes of weights allow to write these indirect seminorms in direct form, that is, in terms of the function itself rather than its Hankel transform. In this paper, we give fairly general conditions on which ensure that the Zemanian spaces ℬμ and ℋμ   are dense in . These conditions are shown to be satisfied by the weights giving rise to direct seminorms of the so-called type II.

Weak compactness and the Eisenfeld-Lakshmikantham measure of nonconvexity

In this article, weakly compact subsets of real Banach spaces are characterized in terms of the Cantor property for the Eisenfeld-Lakshmikantham measure of nonconvexity. This characterization is applied to prove the existence of fixed points for condensing maps, nonexpansive maps, and isometries without convexity requirements on their domain.Mathematics Subject Classification 2010: Primary 47H10; Secondary 46B20, 47H08, 47H09.

A Property Characterizing Montel Hankel-K{Mp} Spaces*

The family of Hankel-K{Mp } spaces includes a number of test function spaces arising in the theory of the generalized Hankel transformation and can be considered as an analogue in this setting of the Gelfand-Shilov K{Mp } spaces. In this work we exhibit a property characterizing those Hankel-K{Mp } spaces which are Montel