Related papers: On the real differential of a slice regular functi…

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…

Differentiable real function reproducing primes up to a given number and having a differentiable inverse function is constructed. This inverse function is compared with the Riemann-Von Mangoldt exact expression for the number of primes not…

We construct a counterexample to a well-known extension theorem for slice regular functions, which motivates us to develop a theory of Riemann slice-domains by introducing a new topology on quaternions. By some paths describing axial…

The notion of constructible functions in the setting of tame real geometry has been introduced by Cluckers and Dan Miller in their work on parametric integration of globally subanalytic functions. A function on a globally subanalytic set is…

In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense…

The problem of reconstruction a function from spherical means is at the heart of several modern imaging modalities and other applications. In this paper we derive universal back-projection type reconstruction formulas for recovering a…

The theory of slice regular functions of a quaternionic variable, introduced in 2006 by Gentili and Struppa, extends the notion of holomorphic function to the quaternionic setting. This fast growing theory is already rich of many results…

Let X=H\G be a homogeneous spherical variety for a split reductive group G over the integers o of a p-adic field k, and K=G(o) a hyperspecial maximal compact subgroup of G=G(k). We compute eigenfunctions ("spherical functions") on X=X(k)…

In this article we investigate harmonicity, Laplacians, mean value theorems and related topics in the context of quaternionic analysis. We observe that a Mean Value Formula for slice regular functions holds true and it is a consequence of…

There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…

In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part…

In the previous paper [25], Stolarsky's invariance principle, known for point distributions on the Euclidean spheres [27], has been extended to the real, complex, and quaternionic projective spaces and the octonionic projective plane.…

We ask whether every polynomial function that is non-negative on a real algebraic curve can be expressed as a sum of squares in the coordinate ring. Scheiderer has classified all irreducible curves for which this is the case. For reducible…

The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…

We show that a differential version of the classical Chebyshev-Markov-Stieltjes inequalities holds for a broad family of weight functions. Such a differential version appears to be new. Our results apply to weight functions which are…

In this article, we give an explicit description of the invertible functions on the Drinfeld symmetric space over $K$ a finite extension of $\mathbb{Q}_p$. We identify them with some distribution spaces over the profinite set of…

In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…

Irreducible decomposition of monomial ideals has an increasing number of applications from biology to pure math. This paper presents the Slice Algorithm for computing irreducible decompositions, Alexander duals and socles of monomial…

We prove the following theorem: let $\widetilde{\mathcal R}$ be an expansion of the real field $\overline{\mathbb R}$, such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a "semialgebraic…

Consider a normal function $f$ on the ordinals (i. e. a function $f$ that is strictly increasing and continuous at limit stages). By enumerating the fixed points of $f$ we obtain a faster normal function $f'$, called the derivative of $f$.…