Related papers: Galois Connections for Generalized Functions and R…

This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f:E sqcap F to F which can be lifted to Keller C^k_pi maps f_i:E sqcap F_i to F_i with F_i Banach and F=projlim F_i .…

Motivated by the study of the distribution of zeros of generalized Bessel-type functions, the principal goal of this paper is to identify new research directions in the theory of multiplier sequences. The investigations focus on multiplier…

This paper presents a comprehensive study of a class of functions which approximate 1/|x| for large x but which are finite at the origin. These functions arise naturally in the study of atoms in strong magnetic fields where the so-called…

In this paper we review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations. We show that there are a number of physically interesting cases which cannot be treated using…

Extending the work of Freese, we further develop the theory of generalized trigonometric functions. In particular, we study to what extent the notion of polar form for the complex numbers may be generalized to arbitrary associative…

This paper is the second in a series investigating cartesian closed varieties. In first of these, we showed that every non-degenerate finitary cartesian variety is a variety of sets equipped with an action by a Boolean algebra B and a…

In previous works, we described algorithms to compute the number field cut out by the mod ell representation attached to a modular form of level N=1. In this article, we explain how these algorithms can be generalised to forms of higher…

We study the absolute Galois group by looking for invariants and orbits of its faithful action on Grothendieck's dessins d'enfants. We define a class of functions called Belyi-extending maps, which we use to construct new Galois invariants…

Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are…

Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued…

The problem of computing \emph{the exponent lattice} which consists of all the multiplicative relations between the roots of a univariate polynomial has drawn much attention in the field of computer algebra. As is known, almost all…

Let $\mathbb{K}$ be a number field of degree $k$ and let $\mathcal{O}$ be an order in $\mathbb{K}$. A \emph{generalized number system over $\mathcal{O}$} (GNS for short) is a pair $(p,\mathcal{D})$ where $p \in \mathcal{O}[x]$ is monic and…

Analogical proportions are 4-ary relations that read "A is to B as C is to D". Recent works have highlighted the fact that such relations can support a specific form of inference, called analogical inference. This inference mechanism was…

We solve a functional equation connected to the algebraic characterization of generalized information functions. To prove the symmetry of the solution, we study a related system of functional equations, which involves two homographies.…

Gel'fand triples of test and generalized functionals in Gaussian spaces are constructed and characterized.

Using dynamical methods we give a new proof of the theorem saying that if $A,B,X$ are rational functions of degree at least two such that $A\circ X=X\circ B$ and $\mathbb C(B,X)=\mathbb C(z)$, then the Galois closure of the field extension…

Given $\alpha_1,...,\alpha_m \in (0,1)$, we characterize all integrable functions $f:[0,1]^m \to \mathbb{C}$ satisfying $\int_{A_1 \times ...\times A_m} f =0$ for any collection of disjoint sets $A_1,...,A_m \subseteq [0,1]$ of respective…

We address two interrelated problems concerning the permutation of roots of univariate polynomials whose coefficients depend on parameters. First, we compute the Galois group of polynomials $\varphi(x)\in\mathbb{C}[y_1,\cdots,y_k][x]$ over…

The Generalized Bessel Function (GBF) extends the single variable Bessel function to several dimensions and indices in a nontrivial manner. Two-dimensional GBFs have been studied extensively in the literature and have found application in…

We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions. We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from…