اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدIterated Function Systems in Mixed Euclidean and p-adic Spaces
79
0
0.0
(
0
)
تأليف
Bernd Sing
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained. The relation between the Haar measure and the Hausdorff measure is clarified. Finally, we discus an example in ${Bbb R}times{Bbb Q}sb 2$ and calculate upper and lower bounds for its Hausdorff dimension.
قيم البحث
اقرأ أيضاً
We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the case of the line, there exists a (unique) exotic isometric flow. This contrast
s with the case of higher-dimensional Euclidean spaces, where all isometries of the Wasserstein space preserve the shape of measures. We also study the curvature and various ranks of these spaces.
In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space ($R^d$ with a metric of indefinite signature). We show that a graph is gener
ically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rigidity is always a generic property of a graph in complex space, and give a sufficient condition for it to be a generic property in a pseudo-Euclidean space. Extensions to hyperbolic space are also discussed.
This is the final version, to appear in Commentarii Mathematici Helvetici.
We extend the results in [6] to Besov spaces $B_{p,q}^alpha$ with $p,qin[1,infty]$ and $0<alpha<1$.
Let $d$ be a positive integer, and let $mu$ be a finite measure on $br^d$. In this paper we ask when it is possible to find a subset $Lambda$ in $br^d$ such that the corresponding complex exponential functions $e_lambda$ indexed by $Lambda$ are ortho
gonal and total in $L^2(mu)$. If this happens, we say that $(mu, Lambda)$ is a spectral pair. This is a Fourier duality, and the $x$-variable for the $L^2(mu)$-functions is one side in the duality, while the points in $Lambda$ is the other. Stated this way, the framework is too wide, and we shall restrict attention to measures $mu$ which come with an intrinsic scaling symmetry built in and specified by a finite and prescribed system of contractive affine mappings in $br^d$; an affine iterated function system (IFS). This setting allows us to generate candidates for spectral pairs in such a way that the sets on both sides of the Fourier duality are generated by suitably chosen affine IFSs. For a given affine setup, we spell out the appropriate duality conditions that the two dual IFS-systems must have. Our condition is stated in terms of certain complex Hadamard matrices. Our main results give two ways of building higher dimensional spectral pairs from combinatorial algebra and spectral theory applied to lower dimensional systems.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
