Related papers: Mean value property associated with the Dunkl Lapl…

We study the mean value properties of $\mathbf{p}$-harmonic functions on the first Heisenberg group $\mathbb{H}$, in connection to the dynamic programming principles of certain stochastic processes. We implement the approach of…

We call a kind of mappings induced by a kind of weighted Laplace operator as complex valued kernel $\alpha$-harmonic mappings. In this article, for this class of mappings, the Heinz type lemma is established, and the best Heinz type…

We revisit the well-established regularity estimates on harmonic maps on surfaces to question their independence with respect to the dimension of the target manifold. We are mainly interested in harmonic maps into target ellipsoids, that we…

The aim of the paper is to derive spectral estimates on the eigenvalue moments of the magnetic Dirichlet Laplacian defined on the two-dimensional disk with a radially symmetric magnetic field.

Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.

Let $\psi:{\mathcal{D}}\rightarrow{\mathbf{R}}$ be a harmonic function such that $\Delta\psi(x)=0$ for all $x\in\mathcal{D}\subset{\mathbf{R}}^{n}$. There are then many well-established classical results:the Dirichlet problem and Poisson…

In this paper, we introduce a new higher-order Laplacian operator in the framework of Orlicz-Sobolev spaces, the biharmonic g-Laplacian $$\Delta_g^2 u:=\Delta \left(\dfrac{g(|\Delta u|)}{|\Delta u|} \Delta u\right),$$ where $g=G'$, with $G$…

In this article we prove the equivalence of certain inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian with a classical inequality of Kac. Connections are made via integral transforms including those of Laplace,…

In this paper, we investigate eigenvalues of Laplacian on a bounded domain in an $n$-dimensional Euclidean space and obtain a sharper lower bound for the sum of its eigenvalues, which gives an improvement of results due to A. D. Melas [15].…

The work analyzes the theory of Dunkl operator as a moment differential operator. This last operator generalizes the first one whenever the sequence of moments satisfies appropriate classical properties, classically considered in the…

This work, dealt with the classical mean value theorem and took advantage of it in the fractional calculus. The concept of a fractional critical point is introduced. Some sufficient conditions for the existence of a critical point is…

During the study of the topic of limit summability of functions (introduced by the author in 2001), we encountered some types of functions that are related to the mean value theorem. In this paper, we formally define mean value and…

This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…

In this paper the authors investigate a power mean inequality for a special function which is defined by the complete elliptic integrals.

Let $M$ be a compact, connected Riemannian manifold whose Riemannian volume measure is denoted by $\sigma$. Let $f: M \rightarrow \mathbb{R}$ be a non-constant eigenfunction of the Laplacian. The random wave conjecture suggests that in…

We prove that the zeta-function $\zeta_\Delta$ of the Laplacian $\Delta$ on a self-similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane. We characterise the poles, compute their residues,…

In this paper, we present an approach to the fractional Dunkl Laplacian in a framework emerging from certain reflection symmetries in Euclidean spaces. Our main result is pointwise formulas, Bochner subordination, and an extension problem…

Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on $\mathbb{R}^{N}$. The Dunkl operators are denoted by $T_{j}$ for $1\leq j\leq N$, and the…

In this paper, we establish a mean value result of arithmetic functions over shorter intervals with the Selberg-Delange method using the Hooley-Huxley contour.

Let $G$ be a nonempty bounded domain in a finite-dimensional Euclidean space. The main results are general estimates from below at points from $G$ for an arbitrary subharmonic function $u\not\equiv -\infty$ on the closure of the domain $G$…