Related papers: Green function estimates on complements of low-dim…

Combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis we introduce a new method of spectral analysis on self-similar graphs. We give an…

We discuss Euclidean Green functions on product manifolds P=NxM. We show that if M is compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this…

Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$,…

Let $S_\epsilon$ be a set of $N$ points in a bounded hyperconvex domain in $C^n$, all tending to 0 as$\epsilon$ tends to 0. To each set $S_\epsilon$ we associate its vanishing ideal $I_\epsilon$ and the pluricomplex Green function…

For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_j \text{when} x \to a_j, j=1,...,N \}$. When there…

New exact and asymptotical results for the one particle Green's function of 2D electrons with combined Rashba - Dresselhaus spin - orbit interaction in the presence of in-plane uniform magnetic field are presented. A special case that…

Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in $R^d$. For a positive (respectively, negative) parameter $\gamma$ we consider red-blue matchings that locally minimize (respectively,…

We present a method for accurate evaluation of the Green function $G(\omega,r_1,...,r_d)$ at any real frequency $\omega$ and any lattice vector $(r_1,...,r_d)$ for a $d$-dimensional hypercubic lattice that may have anisotropic couplings…

The present paper, along with its sequel, establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute…

In [BEI] we introduced a Levy process on a hierarchical lattice which is four dimensional, in the sense that the Green's function for the process equals 1/x^2. If the process is modified so as to be weakly self-repelling, it was shown that…

We give a simple proof of a well-known theorem of G\'al and of the recent related results of Aistleitner, Berkes and Seip [1] regarding the size of GCD sums. In fact, our method obtains the asymptotically sharp constant in G\'al's theorem,…

We prove an analogue of a perturbation result for the Dirichlet problem of divergence form elliptic operators by Fefferman, Kenig and Pipher, for the degenerate elliptic operators of David, Feneuil and Mayboroda, which were developed to…

We approximate a Euclidean version of a D+1 dimensional manifold with a bifurcate Killing horizon by a product of a two-dimensional Rindler space and a D-1 dimensional manifold M. We obtain approximate formulas for the Green functions. We…

Given a locally compact, complete metric space $({\rm X},{\sf D})$ and an open set $\Omega\subseteq{\rm X}$, we study the class of length distances $\sf d$ on $\Omega$ that are bounded from above and below by fixed multiples of the ambient…

This letter presents an almost sure convergence of the zeroth-order mirror descent algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provides noisy function value at any desired point. We approximate…

Optimal pointwise estimates are derived for the biharmonic Green function under Dirichlet boundary conditions in arbitrary $C^{4,\gamma}$-smooth domains. Maximum principles do not exist for fourth order elliptic equations and the Green…

For a given second order elliptic operation $\mathcal{L}$ in a domain $\Omega\subset{\mathbb{R}}^\mathbf{N}$, $\mathbf{N}\ $, and a compact set $\mathbf{K}\subset\Omega$, order $\mathbf{N}$-$2$-Ahlfors-David regular, we define the space…

Assume that $p > 1$ and $p - 1 \le \alpha \le p$ are real numbers and $\Omega$ is a non-empty open subset of ${\mathbb R}^n$, $n \ge 2$. We consider the inequality $$ {\rm div} \, A (x, D u) + b (x) |D u|^\alpha \ge 0, $$ where $D =…

For a sparse non-singular matrix $A$, generally $A^{-1}$ is a dense matrix. However, for a class of matrices, $A^{-1}$ can be a matrix with off-diagonal decay properties, i.e. $\lvert A^{-1}_{ij}\rvert$ decays fast to $0$ with respect to…

We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove…