Extension results for slice regular functions of a quaternionic variable

In this paper we prove a new representation formula for slice regular functions, which shows that the value of a slice regular function $f$ at a point $q=x+yI$ can be recovered by the values of $f$ at the points $q+yJ$ and $q+yK$ for any choice of imaginary units $I, J, K.$ This result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a much larger class of domains, called axially symmetric domains. We show, in particular, that axially symmetric domains play, for slice regular functions, the role played by domains of holomorphy for holomorphic functions

Market competition or family ties: Which prevails on Italian CEOs pay?

The paper analyzes the interplay of product market competition and governance on CEO compensation in Italian listed firms from 2000 to 2011 and tests the impact of the 2007-08 financial crisis on pay-performance sensitivity. We argue that important differences both in the level of compensation and its sensitivity to firm performance depend on two conditioning factors: family ownership and source of the competitive pressure. A novel aspect of our paper is that we rely on two definitions of competition: the intensity of import penetration, which accounts for price competition, and the intensity of R&D and advertising expenditures, which captures the oligopolistic nature of competition when products are vertically differentiated. Overall, the compensation of Italian CEOs is positively related to firm performance. Moreover, consistent with our predictions, sensitivity is higher in competitive sectors and the difference between family and non-family CEOs disappear when competition is tough. Family CEOs are significantly less paid than non-family CEOs and their pay is significantly related to firm performance. However, behind this sensitivity we find asymmetric responses to performance changes: while non-family CEOs pay mainly responds to negative changes, family CEOs pay is sensitive only to positive changes. Finally, we find that the 2007 financial crisis reduces the difference between family and non-family CEO by de-creasing the level of their compensation and increasing its responsiveness to performance. Altogether, our results provide supporting evidence to the idea that market competition eventu-ally prevails over family ties even in a family-controlled governance system such as in Ital

Regular Functions on the Space of Cayley Numbers

In this paper we present a new definition of regularity on the space Ç of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions, and we develop the basic elements of a function theory on Ç. Particular attention is given to the structure of the zero sets of such functions

On a Generalization of the Corona Problem

Let g, fl,...., fm EH (A). We provide conditions on fl,...,fm in order that Ig(z) lIfi(z)l+...+Ifm (z)I, for all z in 4, imply that g, or g2, belong to the ideal generated by fl,....,fm in H

A New Theory of Regular Functions of a Quaternionic Variable

In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series

Market Power and Patent Strategies: Evidence from Renaissance Venice

This paper exploits the introduction of the first regularized patent system, which appeared in the Venetian Republic in 1474, to examine the factors shaping inventors\u2019 propensity to use a new form of intellectual property. We combine detailed information on craft guilds and patents in Renaissance Venice and show a negative association between patenting activity and guild statutory norms that strongly restricted entry and price competition. Our analysis shows that the heterogeneity in patenting activity documented by the industrial organization literature is not a special feature of modern technologies, but is rather a persistent phenomenon affected by market power

The Centre-Periphery Dialectics in Eastern Sicily Retail System. An Exploratory Research

This paper aims at scrutinizing from an historical perspective the deep trans-formations shaped by retail spaces and new consumption patterns challenging long-entrenched dichotomies, such as the centre-periphery one. In particular, the exploratory research explores the territorial reconfiguration of the main Eastern Sicily metropol-itan areas, Catania and Messina, from the lens of the retail geography, namely after the diffusion of new suburban retail formats which have completely upset deeply-rooted relations between urban core and suburban rings

The Merchant and the Mathematician: Commerce and Accounting

In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved

Ideals of regular functions of a quaternionic variable

In this paper we prove that, for any $n\in \mathbb N$, the ideal generated by $n$ slice regular functions $f_1,\ldots,f_n$ having no common zeros concides with the entire ring of slice regular functions. The proof required the study of the non-commutative syzygies of a vector of regular functions, that manifest a different character when compared with their complex counterparts.Comment: 13 page