Related papers: The Bohr Theorem for slice regular functions

We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…

Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same…

We prove some formulas relating Cauchy-Riemann operators defined on hypercomplex subspaces of an alternative *-algebra to a differential operator associated with the concept of slice-regularity and to the spherical Dirac operator. These…

This paper has a twofold purpose: on one hand we deepen the study of slice regular functions by studying their behavior with respect to the so-called C-property and anti-C-property. We show that, for any fixed basis of the algebra of…

Luna's etale slice theorem is a useful theorem for the local study of quotients by reductive algebraic groups. In this article, we show that the slice theorem can also be used to study local structures of invariant Hilbert schemes. By using…

Baiocchi et al. generalized a few years ago a classical theorem of Ingham and Beurling by means of divided differences. The optimality of their assumption has been proven by the third author of this note. The purpose of this note to extend…

We define "splitting functions of level l" for any integer l>0. These functions generalize Dwork's splitting functions : they allow us to represent additive characters of order $p^l$. Then we use these functions to obtain a Stickleberger…

We study global properties of quaternionic slice regular functions (also called s-regular) defined on symmetric slice domains. In particular, thanks to new techniques and points of view, we can characterize the property of being one-slice…

We prove a new cross theorem for separately holomorphic functions.

We study the Borel map, which maps infinitely differentiable functions on an interval to the jets of their Taylor coefficients at a given point in the interval. Our main results include a complete description of the image of the Borel map…

In recent years, the study of slice monogenic functions has attracted more and more attention in the literature. In this paper, an extension of the well-known Dirac operator is defined which allows to establish the Lie superalgebra…

A general slice theorem for the action of a Fr\'echet Lie group on a Fr\'echet manifolds is established. The Nash-Moser theorem provides the fundamental tool to generalize the result of Palais to this infinite-dimensional setting. The…

Categories of partial functions have become increasingly important principally because of their applications in theoretical computer science. In this note we prove that the category of partial bijections between sets as an…

In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain \begin{equation*} \Omega_{\gamma}=\bigg\{z\in\mathbb{C} :…

The edge-of-the-wedge theorem in several complex variables gives the analytic continuation of functions defined on the poly upper half plane and the poly lower half plane, the set of points in $\mathbb{C}^d$ with all coordinates in the…

The Brill-Noether Theorem gives necessary and sufficient conditions for the existence of a linear series. Here we consider a general n-fold, etale cyclic cover p of a curve C of genus g and investigate for which numbers r,d a linear series…

We give a short direct proof of Agler's factorization theorem that uses the abstract characterization of operator algebras. the key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional…

We define a very general notion of regularity for functions taking values in an alternative real $*$-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over…

The aim of this paper is to introduce and to study an algebra of almost periodic generalized functions containing the classical Bohr almost periodic functions as well as almost periodic Schwartz distributions

We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The theorem concerns a family of curves on a family of surfaces. It has two parts. The first was proved in that paper.…