Some questions related to fractals
英文摘要：
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Some Open Problems Concerning Orthogonal Polynomials on Fractals and Related Questions
Some Open Problems Concerning Orthogonal Polynomials.
math.CA
A geometric construction for fractal sets and related linear operators
A way to add an extra dimension is briefly discussed.
math.CA
分形圆极大函数及相关局部光滑性的端点估计
Endpoint estimates for the fractal circular maximal function and related local smoothing
本文证明了分形圆极大函数在伸缩集分形维数位于 $[1/2, 1)$ 时缺失的端点估计，并利用双线性方法扩展了分形伸缩集上波动算子局部光滑性估计成立的 $p,q$ 范围。
math.CA
Some remarks about Clifford analysis and fractal sets
Although Clifford analysis is like complex analysis in many ways, there are obvious differences related to noncommutativity, and a few aspects of this are considered here.
math.CA
Happy fractals and some aspects of analysis on metric spaces
By a "happy fractal" we mean a metric space with bounded geometry in the sense of a doubling condition and a lot of paths of finite length, so that any pair of points can be connected by a path whose length is less than or equal to a constant times the distance between the two points. In these notes we consider some examples, related notions, and other aspects of analysis on metric spaces. This includes Lipschitz functions of some positive order and the special class of functions known as "atoms" which are related to singular integral operators.
math.CA
Projections of self-similar and related fractals: a survey of recent developments
In recent years there has been much interest -and progress- in understanding projections of many concrete fractals sets and measures. The general goal is to be able to go beyond general results such as Marstrand's Theorem, and quantify the size of every projection - or at least every projection outside some very small set. This article surveys some of these results and the techniques that were developed to obtain them, focusing on linear projections of planar self-similar sets and measures.
math.CAmath.DS
更多相关论文收起更多论文
关于与“分形山麓”相关的一些显式积分
On some explicit integrals related to "fractal foothills"
本文通过将无限随机游走的完整环计数函数简化为仅计数返回原点的部分环计数函数V，推导出与V相关的多种积分的闭式表达式，并进一步揭示了完整环计数函数与伯努利多项式之间的联系。
math.CAmath.COmath.FA
与Pascal金字塔模素数分形维数相关的完全Bernstein函数
A complete Bernstein function related to the fractal dimension of Pascal's pyramid modulo a prime
本文证明函数$f_r(x)=\log(1+rx)/\log(1+x)$在$0\le r\le 1$时为完全Bernstein函数，在$r\ge 1$时为Stieltjes函数，从而解决了David Bradley的猜想。
math.CAmath.NT
On some explicit integrals related to "fractal mountains"
Loop counting functions $U(x)$ estimate the number of "weighted" loops in a digital representation of $x\in[-1,1]$. Roughly speaking, each $x$ is considered as an infinite walk, where the steps of the walk correspond to digits of $x$. The graph of loop counting functions $U$ has a fractal structure that resembles complex mountain landscapes. In some sense, $U$ allows us to look at random walks globally. These functions may be helpful in the analysis of some hard problems related to the distribution of self-avoiding random walks (SAW) in a multi-dimensional case since SAW closely relate to zero…
math.CAmath.COmath.FA
Generic Hölder level sets on Fractals
Hausdorff dimensions of level sets of generic continuous functions defined on fractals were considered in two papers by R. Balka, Z. Buczolich and M. Elekes. In those papers the topological Hausdorff dimension of fractals was defined. In this paper we start to study level sets of generic $1$-Hölder-$α$ functions defined on fractals. This is related to some sort of "thickness", "conductivity" properties of fractals. The main concept of our paper is $D_{*}(α, F)$ which is the essential supremum of the Hausdorff dimensions of the level sets of a generic $1$-Hölder-$α$ function defined on the frac…
math-phmath.CAmath.MP
