Zobrazeno 1 - 10
of 135
pro vyhledávání: '"Gselmann, Eszter"'
Autor:
Gselmann, Eszter, Iqbal, Mehak
Let $\mathbb{F}\subset \mathbb{K}$ be fields with characteristic zero, $n$ be a positive integer and $\kappa\in \mathbb{K}$. In this paper, we determine those monomials $f\colon \mathbb{F}\to \mathbb{K}$ of degree $n$ for which \[ f(x^{2})= \kappa\cd
Externí odkaz:
http://arxiv.org/abs/2410.07831
Autor:
Gselmann, Eszter, Iqbal, Mehak
The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relatively many results are known. However, even in this case, there are a lot
Externí odkaz:
http://arxiv.org/abs/2403.00518
Iverson (2006) proposed the law of similarity \[ \xi_{s}(\lambda x)= \gamma(\lambda, s)\xi_{\eta(\lambda, s)}(x) \] for the sensitivity functions $\xi_{s}\, (s\in S)$. Compared to the former models, the generality of this one lies in that here $\gamm
Externí odkaz:
http://arxiv.org/abs/2402.07670
Autor:
Fechner, Włodzimierz, Gselmann, Eszter
The paper aims to provide a full characterization of all operators $T\colon \mathscr{P}(\mathbb{C}) \to \mathscr{P}(\mathbb{C})$ acting on the space of all complex polynomials that satisfy the Leibniz rule \[ T(f\cdot g)= T(f)\cdot g+f\cdot T(g) \] f
Externí odkaz:
http://arxiv.org/abs/2311.04671
Let $r$ be a positive integer, $N$ be a nonnegative integer and $\Omega \subset \mathbb{R}^{r}$ be a domain. Further, for all multi-indices $\alpha \in \mathbb{N}^{r}$, $|\alpha|\leq N$, let us consider the partial differential operator $D^{\alpha}$
Externí odkaz:
http://arxiv.org/abs/2309.03572
{Let $N, k$ be positive integers with $k\geq 2$, and $\Omega \subset \mathbb{R}^{N}$ be a domain.} By the well-known properties of the Laplacian and the gradient, we have \[ \Delta(f\cdot g)(x)=g(x) \Delta f(x)+f(x) \Delta g(x)+2\langle \nabla f(x),
Externí odkaz:
http://arxiv.org/abs/2306.02788
Autor:
Gselmann, Eszter, Kiss, Gergely
In this sequence of work we investigate polynomial equations of additive functions. We consider the solutions of equation \[ \sum_{i=1}^{n}f_{i}(x^{p_{i}})g_{i}(x)^{q_{i}}= 0 \qquad \left(x\in \mathbb{F}\right), \] where $n$ is a positive integer, $\
Externí odkaz:
http://arxiv.org/abs/2303.03306
Autor:
Gselmann, Eszter, Iqbal, Mehak
In this paper we consider generalized monomial functions $f, g\colon \mathbb{F}\to \mathbb{C}$ (of possibly different degree) that also fulfill \[ f(P(x))= Q(g(x)) \qquad \left(x\in \mathbb{F}\right), \] where $P\in \mathbb{F}[x]$ and $Q\in \mathbb{C
Externí odkaz:
http://arxiv.org/abs/2212.10115
Autor:
Gselmann, Eszter, Kiss, Gergely
The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the following type
Externí odkaz:
http://arxiv.org/abs/2211.03605
In one of our former papers {\it Endomorphisms of the measure algebra of commutative hypergroups arXiv:2204.07499 we considered exponential monomials on hypergroups and higher order derivations of the corresponding measure algebra. Continuing with th
Externí odkaz:
http://arxiv.org/abs/2209.08805