相关论文: Permuting triderivations and permuting trihomomorp…

Each family of Gauss hypergeometric functions $$ f_n={}_2F_1(a+\epsilon_1n, b+\epsilon_2n ;c+\epsilon_3n; z), $$ for fixed $\epsilon_j=0,\pm1$ (not all $\epsilon_j$ equal to zero) satisfies a second order linear difference equation of the…

We produce nontrivial asymptotic estimates for shifted sums of the form $\sum a(h)b(m)c(2m-h)$, in which $a(n),b(n),c(n)$ are un-normalized Fourier coefficients of holomorphic cusp forms. These results are unconditional, but we demonstrate…

For a field $\mathbb{F}$, what are all functions $f \colon \mathbb{F} \rightarrow \mathbb{F}$ that satisfy the functional equation $f \left( (x+y)/(x-y) \right) = (f(x) + f(y))/(f(x) - f(y))$ for all $ x \neq y$ in $\mathbb{F}$? We solve…

In this paper, we investigate the delay differential equations of Malmquist type of form \begin{equation*} w(z+1)-w(z-1)+a(z)\frac{w'(z)}{w(z)}=R(z, w(z)),~~~~~~~~~~~~~~(*) \end{equation*} where $R(z, w(z))$ is an irreducible rational…

We prove a version of the Beurling-Malliavin multiplier theorem. This version is formulated here in a simplified form. Let $u\not\equiv -\infty$ and $M\not\equiv -\infty$ be a pair of subharmonic functions on the complex plane $\mathbb C$…

For two meromorphic functions $ f $ and $ g $, the equation $ f^m+g^m=1 $ can be regarded as Fermat-type equations. Using Nevanlinna theory for meromorphic functions in several complex variables, the main purpose of this paper is to…

We introduce notions of compactness and weak compactness for multilinear maps from a product of normed spaces to a normed space, and prove some general results about these notions. We then consider linear maps $T:A\to B$ between Banach…

In this work, we develop systematically the ``Dirichlet Hopf algebra of arithmetics'' by dualizing addition and multiplication maps. We study the additive and multiplicative antipodal convolutions which fail to give rise to Hopf algebra…

In this article, we present a new subadditivity behavior of convex and concave functions, when applied to Hilbert space operators. For example, under suitable assumptions on the spectrum of the positive operators $A$ and $B$, we prove that…

It is shown that if the equation \begin{equation*} f(z+1)^n=R(z,f), \end{equation*} where $R(z,f)$ is rational in both arguments and $\deg_f(R(z,f))\not=n$, has a transcendental meromorphic solution, then the equation above reduces into one…

Let $F(x, y)$ be a binary form with integer coefficients, degree $n\geq 3$ and irreducible over the rationals. Suppose that only $s + 1$ of the $n + 1$ coefficients of $F$ are nonzero. We show that the Thue inequality $|F(x,y)|\leq m$ has…

In this paper, we obtain the general solution of the following functional equation f(3x + y + z) + f(x + 3y + z) + f(x + y + 3z) + f(x) + f(y) + f(z) = 6f(x + y + z): We establish the Hyers-Ulam-Rassias stability of the above functional…

We study solutions and approximate solutions of the multiplicative Sincov equation $$T(f, h) = T(f, g)T(g, h)$$ for mapping $T$ taking values in a commutative Banach algebra.

We here present a method of performing integrals of products of spherical Bessel functions (SBFs) weighted by a power-law. Our method, which begins with double-SBF integrals, exploits a differential operator $\hat{D}$ defined via Bessel's…

In this work we are concerned with Fefferman-Stein type inequalities. More precisely, given an operator $T$ and some $p$, $1<p<\infty$, we look for operators $\mathcal{M}$ such that the inequality $$\int |Tf|^pw\leq C\int |f|^p…

The existence of the meromorphic solutions to Fermat type delay-differential equation \begin{equation} f^n(z)+a(f^{(l)}(z+c))^m=p_1(z)e^{a_1z^k}+p_2(z)e^{a_2z^k}, \nonumber \end{equation} is derived by using Nevanlinna theory under certain…

This paper continues an earlier work on the structure of solutions to two classes of functional equation. Let $Z$ be a compact Abelian group and $U_1$, \ldots, $U_k \leq Z$ be closed subgroups. Given $f:Z\to\mathbb{T}$ and $w \in Z$, one…

The aim of this paper is to pursue the investigation of the phase retrieval problem for the fractional Fourier transform $\ff\_\alpha$ started by the second author. We here extend a method of A.E.J.M Janssen to show that there is a…

We write expressions connected with numerical differentiation formulas of order $2$ in the form of Stieltjes integral, then we use Ohlin lemma and Levin-Stechkin theorem to study inequalities connected with these expressions. In particular,…

This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…