Related papers: Landen inequalities for zero-balanced hypergeometr…
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case…
We prove the following theorems: 1) The Laurent expansions in epsilon of the Gauss hypergeometric functions 2F1(I_1+a*epsilon, I_2+b*epsilon; I_3+p/q + c epsilon; z), 2F1(I_1+p/q+a*epsilon, I_2+p/q+b*epsilon; I_3+ p/q+c*epsilon;z),…
In this note we deal with some inequalities for the tangent function that are valid for $x$ in $(-\pi/2,\pi/2)$. These inequalities are optimal in the sense that the best values of the exponents involved are obtained.
In this paper, we study surfaces $z=\varphi(x,y)$ in Euclidean space that satisfy the equation $\varphi_{xx}+\varphi_{yy}=\frac{\Lambda}{2}$ where $\Lambda\in\r$ is a real constant. We classify these surfaces when they are the zero level…
We provide new direct methods to establish symmetrization results in the form of mass concentration (i.e., integral) comparison for fractional elliptic equations of the type $(-\Delta)^{s}u=f$ $(0<s<1)$ in a bounded domain $\Omega$,…
We consider the Dirichlet problem for two types of degenerate elliptic Hessian equations . New results about solvability of the equations in the $C^{1,1}$ space are provided.
Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type algebraic varieties over finite fields and consequently study…
The double-layer potential plays an important r$\hat{\rm o}$le in solving boundary value problems of elliptic equations. Here, in this paper, we aim at introducing and investigating double layer potentials for a generalized bi-axially…
In this article we find the general, exact solution for the gravitational field equations for diagonal, vacuum, separable metrics. These are metrics each of whose terms can be separated into functions of each space-time variable separately.…
Let $E,F$ be Banach spaces. In the case that $F$ is reflexive we give a description for the solutions $(f,g)$ of the Banach-orthogonality equation $$\langle f(x),g(\alpha)\rangle=\langle x,\alpha\rangle\hspace{10mm}\forall x\in E,\forall…
This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the…
We study maximal functions related to homogeneous polynomial hypersurfaces in $\mathbb{R}^3$. In a sense made precise in this paper, the region of $(p,q)$ for which we obtain $L^p\rightarrow L^q$ boundedness is optimal up to the endpoints…
The main purpose of this work is to study uniform regularity estimates for a family of elliptic operators $\{\mathcal{L}_\varepsilon, \varepsilon>0\}$, arising in the theory of homogenization, with rapidly oscillating periodic coefficients.…
We study sampling properties of the zero set of the Gaussian entire function on Fock spaces. Firstly, we relax Seip and Wallst\'en's density and separation conditions for sampling sets on Fock spaces to obtain weighted inequalities for sets…
Evaluation of low degree hypergeometric polynomials to zero defines an algebraic hypersurface in the affine space of the free parameters and the argument. This article investigates the algebraic surfaces 2F1(-N,b;c;z)=0 for N=3 and N=4. As…
We consider the three most important equations of hypergeometric type, ${}_2F_1$, ${}_1F_1$ and ${}_1F_0$, in the so-called degenerate case. In this case one of the parameters, usually denoted $c$, is an integer and the standard basis of…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
Algorithms for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. The algorithms are based on global fixed point iterations which apply to families of functions satisfying…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All…
A scale of the Frechet spaces of exponential type entire functions of one complex variable is considered. Certain special properties of subsets of these spaces consisting of Laguerre entire functions, which are obtained as uniform limits on…