相关论文: Discrete harmonic functions for non-symmetric Lapl…

Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator.…

Enumeration of walks with small steps in the quadrant has been a topic of great interest in combinatorics over the last few years. In this article, it is shown how to compute exact asymptotics of the number of such walks with fixed start-…

In this article, we study harmonic symmetries on the compact locally conformally K\"{a}hler manifold $M$ of $dim_{\mathbb{C}}=n$. The space of harmonic symmetries is a subspace of harmonic differential forms which defined by the kernel of a…

We investigate an approach for the numerical solution of differential equations which is based on the perfect discretization of actions. Such perfect discretizations show up at the fixed points of renormalization group transformations. This…

We consider a number of combinatorial problems in which rational generating functions may be obtained, whose denominators have factors with certain singularities. Specifically, there exist points near which one of the factors is asymptotic…

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian…

We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…

We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are…

We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…

The aim of this paper is two-fold: first, we look at the fractional Laplacian and the conformal fractional Laplacian from the general framework of representation theory on symmetric spaces and, second, we construct new boundary operators…

Using properties of harmonic functions in multidimensional space, we transform the Hartree-Fock eigenvalue problem into a more tractable eigenvalue problem in which the Laplacian is eliminated. This new formulation may facilitate the…

The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…

We construct a nonlinear lattice that has a particular symmetry in its potential function consisting of long-range pairwise interactions. The symmetry enhances smooth propagation of discrete breathers, and it is defined by an invariance of…

We study directed weighted graphs which are invariant under a nilpotent and cocompact group action. In particular, we consider the conic section K of the set of positive harmonic functions. We characterise the set of extreme points of the…

It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be…

We study composition operators on spaces of holomorphic Lipschitz functions defined on the open unit ball of a complex Banach space. Our approach is based on the linearization of the symbol through the holomorphic Lipschitz-free spaces,…

The computation of the partition function in certain quantum field theories, such as those of the Argyres-Douglas or Minahan-Nemeschansky type, is problematic due to the lack of a Lagrangian description. In this paper, we use the…

It is proved the existence of nonclassical solutions of the Neumann problem for the harmonic functions in the Jordan rectifiable domains with arbitrary measurable boundary distributions of normal derivatives. The same is stated for the…

We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to H\"ormander's support theorem for…

Enumeration of planar lattice walks is a classical topic in combinatorics, at the cross-roads of several domains (e.g., probability, statistical physics, computer science). The aim of this paper is to propose a new approach to obtain some…