Related papers: Triakis Solids and Harmonic Functions
We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…
In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic…
We describe the set of bounded harmonic functions for the Heckman--Opdam Laplacian, when the multiplicity function is larger than 1/2. We prove that this set is a vector space of dimension the cardinality of the Weyl group. We give some…
We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on…
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
The space forms, the complex hyperbolic spaces and the quaternionic hyperbolic spaces are characterized as the harmonic manifolds with specific radial eigenfunctions of the Laplacian.
In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…
This article gives necessary and sufficient conditions for the dual representation of Rockafellar in (Integrals which are convex functionals. II, Pacific J. Math., 39:439--469, 1971) for integral functionals on the space of continuous…
The Laplace equation in three dimensional Euclidean space is $R$-separable in bi-cyclide coordinates leading to harmonic functions expressed in terms of Lam\'e-Wangerin functions called internal and external bi-cyclide harmonics. An…
The purpose of this paper is mostly to present conjectures that extend, to the ``triangular partition'' context (partitions ``under any line'' in the terminology of Blaziak-Haiman-Morse-Pun-Seelinger), properties of Frobenius of…
In this course of lectures we give an account of the growth theory of subharmonic functions, which is directed towards its applications to entire functions of one and several complex variables.
We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…
We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for $\mathbb{CP}^n$ and $\mathbb{CH}^n$,…
In this paper we classify those three-dimensional Riemannian Lie groups which admit harmonic morphisms to surfaces.
We show that if $p \colon M \to N$ is a normal Riemannian covering, with $N$ closed, and $M$ has exponential volume growth, then there are non-constant, positive harmonic functions on $M$. This was conjectured by Lyons and Sullivan in…
We prove inequalities involving intrinsic and extrinsic radii and diameters of tetrahedra.
A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for…
A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical symmetries and physical equivalence of noncommutative systems with the same energy spectrum are investigated and discussed. General solutions of…
We introduce and study properties of certain new multifunctional harmonic spaces in the upper halfspace.We prove several sharp embedding theorems for such multifunctional spaces,these results are new even in the case of a single function.
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.