Related papers: On additive functions with additional derivation p…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…
Given a function f in the exterior of a convex curve in the real plane, we prove that if the restrictions of f to the tangent lines to the curve extend as entire functions, then the function f is an entire function of two variables.
Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…
A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to…
The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular…
In this paper, we prove a new generalized Mikhlin multiplier theorem whose conditions are given with respect to fractional derivatives in integral forms with two different integration intervals. We also discuss the connection between…
We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
In the present paper, several properties concerning generalized derivatives of multifunctions implicitly defined by set-valued inclusions are studied by techniques of variational analysis. Set-valued inclusions are problems formalizing the…
We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves…
Let $f(n)$ be a strongly additive complex valued arithmetic function. Under mild conditions on $f$, we prove the following weighted strong law of large numbers: if $ X,X_1,X_2,... $ is any sequence of integrable i.i.d. random variables,…
We extend the classical Lebesgue and Fubini differentiation theorems to functions of several variables, using the notions of joint derivative and joint monotonicity. Our first main result shows that for a function $f$ of bounded variation,…
In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional…
We characterize all pairs $(\mathcal{A}$,$\mathcal{B})$ of generalized Riemann differences for which $\mathcal{A}$-differentiability implies $\mathcal{B}$-differentiability. Two generalized Riemann derivatives $\mathcal{A}$ and…
The product of any finite number of factorial Schur functions can be expanded as a $Z[y]$-linear combination of Schur functions. We give a rule for computing the coefficients in such an expansion which generalizes a specialization of the…
In this paper, we introduce a new class of derivations that generalizes skew derivations and semi-derivations, and we call it ``skew semi-derivation". Further, we present a study of the conditions under which this type of multiplicative…
The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation iff they must remain occurrences of the same…
In this note the well-ordering principle for the derivative of normal functions on ordinals is shown to be equivalent to the existence of arbitrarily large countable coded omega-models of the well-ordering principle for the function.
In this paper, we will show that if for every nonlinear complex irreducible character of a finite group G, some multiple of it is induced from an irreducible character of some proper subgroup of G, then G is solvable. This is a…