Related papers: On Laplace transform on semitattices
We study integral functionals defined on scalar Sobolev spaces of the form $$E[f]:u\mapsto \int_\Omega f(x,u(x),\nabla u(x)) d x,$$ with an emphasis on the non-convex case, and the difficulties it involves to prevent the Lavrentiev…
In this paper, we present a concise development of the well-studied theory of trace class operators on infinite dimensional (separable) Hilbert spaces suitable for an advanced undergraduate, as well as a construction of the inverse…
The aim of this short article is to generalize, with a slighthly different point of view, some new results concerning the fractional powers of the Laplace operator to the setting of Nilpotent Lie Groups and to study its relationship with…
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
We show that, in addition to SO(4), the Hubbard model at half filling on a bipartite lattice has a group of discrete symmetries and transformations. A unique Hubbard-Stratonovich decomposition of the interaction term, incorporating both…
In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…
We characterize the polytopes in $\mathbb{R}^d$ (not necessarily convex or connected ones) which multi-tile the space by translations along a given lattice. We also give a necessary and sufficient condition for two polytopes in…
For a class of non compact Riemannian manifolds with ends, we give pseudo-differential expansions of bounded functions of the semi-classical Laplacian and study related Lp boundedness properties.
Complemented lattices and uniquely complemented lattices are very important, not only in mathematics, but also in physics, biology, and even in social sciences. They have been investigated for a long time, especially by Huntington,…
The status of the transverse lattice formulation of light-front QCD is reviewed. It is explained how confinement arises in this formulation for large lattice spacing. The nonperturbative renormalization procedure is outlined in general and…
A semi-isotropic space is a real affine 3-space endowed with the non-degenerate metric dx^{2}-dy^{2}. The main purpose of this paper is to describe the surfaces of revolution in the semi-isotropic space that satisfy some equations in terms…
We prove that quasi-morphisms and quasi-states on a closed integral symplectic manifold descend under symplectic reduction to symplectic hyperplane sections. Along the way we show that quasi-morphisms that arise from spectral invariants are…
We give a brief survey for the recent development of inverse scattering theory on non-compact Riemannian manifolds. The main theme is the reconstruction of the manifold and the metric from the scattering matrix.
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
We introduce abstract net spaces on directed sets and prove their embedding and interpolation properties. Typical examples of interest are lattices of irreducible unitary representations of compact Lie groups and of class I representations…
This is not a new result. Purpose of this work is to describe a method to search the analytical expression of the general real solution of the two-dimensional Laplace differential equation. This thing is not easy to find in scientific…
We consider lattices of regular sets of non negative integers, i.e. of sets definable in Presbuger arithmetic. We prove that if such a lattice is closed under decrement then it is also closed under many other functions: quotients by an…
We give an account on what is known on the subject of permutation matchings, which are bijections of a finite regular semigroup that map each element to one of its inverses. This includes partial solutions to some open questions, including…
Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus singularities. Each marked point is endowed with…
It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…