Related papers: The Bohr Theorem for slice regular functions

The theory of quaternionic slice regular functions was introduced in 2006 and successfully developed for about a decade over symmetric slice domains, which appeared to be the natural setting for their study. Some recent articles paved the…

We prove the following generalisation of Bohr theorem : let $K\subset\mathbb C$ a continuum, $(F_n)_n$ its Faber polynomials, $\Omega_R=\{\Phi_K<R\}, (R>1)$ the levels sets of the Green function; then there exists $R_0>1$ such that for any…

In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.

A promising theory of quaternion-valued functions of one quaternionic variable, now called slice regular functions, has been introduced in 2006. The basic examples of slice regular functions are power series centered at 0 on their balls of…

We start with a bijective proof of Schur's theorem due to Alladi and Gordon and describe how a particular iteration of it leads to some very general theorems on colored partitions. These theorems imply a number of important results,…

Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results in a reformulated "distance form" version and…

In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the…

We study Bohr type inequalities within the framework of fractional calculus. Using Riemann Liouville fractional differential and integral operators, we establish generalized Bohr radii for analytic functions in the unit disk, including the…

Recently, fiber bundle theory has been widely used in the study of the slice regular functions and continuing with this line of research, the present work shows that the quaternionic slice regular Bergman space is the base space of a…

We prove that the partition function associated to a perturbation of the semi-classical harmonic oscillator is the Borel sum of its semi-classical expansion.

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been…

The primary objective of this paper is to establish several sharp results concerning the Bohr inequality, the refined Bohr inequality, and the improved Bohr inequality for the classes of analytic functions and harmonic mappings defined on…

We generalize the representation formula from slice-domains of regularity to general Riemann slice-domains. This result allows us to extend the $*$-product of slice regular functions on axially symmetric domains to certain Riemann…

In this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr type inequalities for such functions.

In this paper we show that the real differential of any injective slice regular function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato, and it is obtained thanks, in…

Here we simplify the proof of the de Rham theorem for Schwartz functions on affine Nash manifolds and generalize the result to the case of non affine Nash manifolds.

This paper considers the Fourier transform over the slice of the Boolean hypercube. We prove a relationship between the Fourier coefficients of a function over the slice, and the Fourier coefficients of its restrictions. As an application,…

In this paper, we define a class of slice Dirac-regular mappings of several variables over Clifford algebras, based on the concept of O(3)-stem mappings. We prove that the slice mappings vanish under the slice Dirac operator, which is…

This paper explores generalized slice monogenic functions by introducing their operator symbols, representation formula, and integral formula. The study extends the Teodorescu transform to a broader class of theorems and inferences,…

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…