Related papers: Extending the Veblen Function

This is the second in a series of papers on natural modification of the normal tractor connection in a parabolic geometry, which naturally prolongs an underlying overdetermined system of invariant differential equations. We give a short…

A classical result due to Bochner characterizes the classical orthogonal polynomial systems as solutions of a second-order eigenvalue equation. We extend Bochner's result by dropping the assumption that the first element of the orthogonal…

A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order $0$ as well as evaluating Schl\"{o}milch and Fourier--Bessel expansions in $\mathcal{O}(N(\log N)^2/\log\!\log N)$ operations. The…

We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…

The problem is considered as to whether a monotone function defined on a subset P of a Euclidean space can be strictly monotonically extended to the whole space. It is proved that this is the case if and only if the function is {\em…

This paper describes a novel method to approximate the polynomial coefficients of regression functions, with particular interest on multi-dimensional classification. The derivation is simple, and offers a fast, robust classification…

Exploiting the similarities between the Helmholtz wave equation and the Klein-Gordon equation, the former is linearized using the Feschbach-Villars procedure used for linearizing the Klein-Gordon equation. Then the Foldy-Wouthuysen…

We consider Bergman spaces and variations of them in one or several complex variables. For some domains we show that in these spaces the generic function is totally unbounded and hence non - extendable. We also show that the generic…

We generalize the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. A key property of this invariant is its semi-additivity on short exact sequences. We show how to…

In this note the well-ordering principle for the derivative of normal functions on ordinals is shown to be equivalent to the existence of arbitrarily large countable coded omega-models of the well-ordering principle for the function.

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by…

We prove a classification of additive polynomial superfunctors, which allows us to compute some extensions of a superfunctor of the form $F \circ A$ where $F$ is a classical polynomial functor and $A$ is additive. We get a formula which…

A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function…

In this article we investigate whether the addition-free theta functions form a canonical notation system for the linear versions of Friedman's well-partial-orders with the so-called gap-condition over a finite set of labels. Rather…

We introduce a framework for ordinal notation systems, present a family of strong yet simple systems, and give many examples of ordinals in these systems. While much of the material is conjectural, we include systems with conjectured…

Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…

In this report, we consider extended real-valued functions on some real vector space. Gerstewitz functionals are used to construct all translative functions. We derive formulas for translative functions which are lower semicontinuous,…

Let $X$ and $Y$ be Banach or normed linear spaces and $F\subset X$ a closed set. We apply our recent extension theorem for vector-valued Baire one functions arXiv:1512.03717 to obtain an extension theorem for vector-valued functions…

We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our…

We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a…