Related papers: On structure of $L^2$-harmonic functions for one-d…
We present a first-principles methodology, within the context of linear-response theory, that greatly facilitates the perturbative study of physical properties of metallic crystals. Our approach builds on ensemble density-functional theory…
We construct new explicit proper r-harmonic functions on the standard n-dimensional sphere S^n and hyperbolic space H^n for any r\ge 1 and n\ge 2.
This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…
In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for…
Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial…
In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to…
We investigate a conformal-like transformation for which the spacetime interval is invariant.
We prove estimates of a $p$-harmonic measure, $p \in (n-m, \infty]$, for sets in $\mathbf{R}^n$ which are close to an $m$-dimensional hyperplane $\Lambda \subset \mathbf{R}^n$, $m \in [0,n-1]$. Using these estimates, we derive results of…
In this note we explore the structure of the diffusion metric of Coifman-Lafon determined by fractional dyadic Laplacians. The main result is that, for each ${t>0}$, the diffusion metric is a function of the dyadic distance, given in…
We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…
The cross section for semi-inclusive deep inelastic scattering can be decomposed in terms of 18 structure functions. At low transverse momentum of the detected hadron, the structure functions can be expressed in terms of…
We develop notions of integrable functions within the theory of schemic motivic integration.
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
A universal description of correlation functions of one-dimensional anyonic gapless systems in the low-momentum regime is presented. We point out a number of interesting features, including universal oscillating terms with frequency…
The main purpose of this paper is to present a number of analytic and geometric properties of the $l$-function and the reduced volume of Perelman, including in particular the monotonicity, the upper bound and the rigidities of the reduced…
No functions class for general measurable sets classes are known whose functions have the property of differentiability of integrals associated to such sets classes. In this paper,we give some subspaces of $L^s$ with $1<s<\infty$, whose…
The celebrated Almgren monotonicity formula for harmonic functions $u:\mathbb{R}^n \rightarrow \mathbb{R}$ says that its $L^2-$energy concentrated on a sphere of radius $r$, when measured in a suitable sense, is non-decreasing: if $u$…
We study the theoretical foundations of composition in diffusion models, with a particular focus on out-of-distribution extrapolation and length-generalization. Prior work has shown that composing distributions via linear score combination…