Related papers: Exploring Functional Identities: From Division Rin…

The purpose of this paper is to characterize several classes of functional identities involving inverses with related mappings from a unital Banach algebra $\mathcal{A}$ over the complex field into a unital $\mathcal{A}$-bimodule…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.

In this paper, we study some extended hypergeometric functions from matrix point of view. We have given the integral representations of these matrix functions. Finally, we obtain some generating function relations using fractional…

We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algebra applied to determinantal ideals of matrices over…

For a fixed prime we prove structure theorems for the kernel and the image of the map that attaches to any differential modular function its differential Fourier expansion. The image of this map, which is the ring of differential Fourier…

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…

We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…

We introduce the concept of fractels for functions and discuss their analytic and algebraic properties. We also consider the representation of polynomials and analytic functions using fractels, and the consequences of these representations…

The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…

Let A be the integral closure of the ring of polynomials CC[t], within the field of algebraic functions in one variable. We show that A interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a…

Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.

We study the differential identities of the algebra $M_k(F)$ of $k\times k$ matrices over a field $F$ of characteristic zero when its full Lie algebra of derivations, $L=\mbox{Der}(M_k(F))$, acts on it. We determine a set of 2 generators of…

This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to…

In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…

In this book i treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However, noncommutativity of a product creates a…

It is shown that commutator identities on associative algebras generate solutions of linearized integrable equations. Next, a special kind of the dressing procedure is suggested that in a special class of integral operators enables to…

Let $n\geq 3$ be an integer. Let $\mathcal{D}$ be a division ring with char$(\mathcal{D})>n$ or char$(\mathcal{D})=0$. Let $\mathcal{R}=M_m(\mathcal{D})$ be a ring of $n\times n$ matrices over $D$, $m\geq 2$. The main theorem in the paper…

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…