Related papers: The algebra of slice functions

We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings,…

The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to…

The main objects of study in this paper are those functionals that are analytic in the sense that they annihilate the non-commutative disc algebra. In the classical univariate case, a theorem of F. and M. Riesz implies that such functionals…

In the past few years, the theory of slice monogenic functions has been developed rapidly mainly motivated by the applications to an elegant functional calculus for non-commuting operators. In this article, we introduce the Teodorescu…

It is proved the existence of large algebraic structures \break --including large vector subspaces or infinitely generated free algebras-- inside, among others, the family of Lebesgue measurable functions that are surjective in a strong…

In their recent work, Gentili and Struppa proposed a different quaternionic analogue of the notion of holomorphic functions in the complex plane, called \textit{slice regular functions}, which has led to several analogues of classical…

Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel…

We compute the K-theory of ring C*-algebras for polynomial rings over finite fields. The key ingredient is a duality theorem which we had obtained in a previous paper. It allows us to show that the K-theory of these algebras has a ring…

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 a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both the theory of monogenic functions and of slice monogenic functions with values in a Clifford algebra.…

We present some new relations between the Cauchy-Riemann operator on the real Clifford algebra $\mathbb R_n$ of signature $(0,n)$ and slice-regular functions on $\mathbb R_n$. The class of slice-regular functions, which comprises all…

We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out…

The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.

In this research, we study zeroes of weakly slice regular functions within the framework of several quaternionic variables, specifically focusing on non-axially symmetric domains. Our recent work introduces path-slice stem functions, along…

This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…

We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…

In this paper we study division algebras over the function fields of curves over $\Q_p$. The first and main tool is to view these fields as function fields over nonsingular $S$ which are projective of relative dimension 1 over the $p$ adic…

We study (von Neumann) regular $^*$-subalgebras of $B(H)$, which we call R$^*$-algebras. The class of R$^*$-algebras coincides with that of "E$^*$-algebras that are pre-C$^*$-algebras" in the sense of Z. Sz\H{u}cs and B. Tak\'acs. We give…

Let $L$ be a solvable Lie algebra of dimension less than or equal to 4 over finite fields. We compute and record, in explicit symbolic form, the zeta functions enumerating subalgebras or ideals of $L$, and study their properties. We also…

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…