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In weighted Orlicz type spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
We review some of the basic mathematical results about density functional theory.
This is the revised version of the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory,…
A new functional model for pairs of commuting isometries is described. Intertwining operators between such models are then studied in order to approach the classification of invariant subspaces of such pairs.
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
In this paper we propose a new refined shear deformation plate theory which possesses a series of desirable features, the most salient of which are as follows: (i) The loads, which are generally considered to be applied on the middle…
The focus of this paper is providing a description of the spaces of counting functions on free monoids and groups and of the Brooks space. These results have been obtained in an earlier publication, however we propose an alternative,…
Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet…
In this paper we consider the approximation of functions by radial basis function interpolants. There is a plethora of results about the asymptotic behaviour of the error between appropriately smooth functions and their interpolants, as the…
We introduce a general class of (quasi-)interpolants of functions defined on a Bravais lattice, and establish several technical results for these interpolants that are crucial ingredients in the analysis of atomistic models and…
In this paper we present a geometrical framework to study the uniformity of a composite material by means of double groupoid theory. The notions of vertical and horizontal uniformity are introduced, as well as other weaker ones that allows…
In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.
Density functional theory for a simple model of dendrimers is proposed. The theory is based on fundamental measure theory which accounts for the hard-sphere repulsion of the segments and on the Wertheim first-order perturbation theory for…
For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the…
We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.
The foundations of forcing theory are reworked to streamline the presentation and to show how the most basic results are applicable in very general contexts.
We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions…
A formal description of a functional analysis approach to the Riemann zeta-functional equation that provides in principle an infinity of different proofs based on work by the author on the existence of dilation-invariant unitary operators…