اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAlmost-nowhere intersection of Cantor sets, and sufficient sampling of their cumulative distribution functions
67
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant measure associated with their iterated function systems. Under appropriate assumptions, we identify sampling schemes of such CDFs, meaning that the underlying Cantor set can be reconstructed from sufficiently many samples of its CDF. To this end, we prove that two Cantor sets have almost-nowhere (with respect to their respective invariant measures) intersection.
قيم البحث
اقرأ أيضاً
In this paper, we study $C^{zeta}$-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in term
s of standard calculus, so we must involve local fractional derivatives. We have generalized the $C^{zeta}$-calculus on the generalized Cantor sets known as middle-$xi$ Cantor sets. We have suggested a calculus on the middle-$xi$ Cantor sets for different values of $xi$ with $0<xi<1$. Differential equations on the middle-$xi$ Cantor sets have been solved, and we have presented the results using illustrative examples. The conditions for super-, normal, and sub-diffusion on fractal sets are given.
We consider inductive limits of weighted spaces of holomorphic functions in the unit ball of $mathbb C^n$. The relationship between sets of uniqueness, weakly sufficient sets and sampling sets in these spaces is studied. In particular, the equivalenc
e of these sets, under general conditions of the weights, is obtained.
We provide a sufficient condition for sets of mobile sampling in terms of the surface density of the set.
In this paper necessary and sufficient conditions are deduced for the starlikeness of Bessel functions of the first kind and their derivatives of the second and third order by using a result of Shah and Trimble about transcendental entire functions w
ith univalent derivatives and some Mittag-Leffler expansions for the derivatives of Bessel functions of the first kind, as well as some results on the zeros of these functions.
We discuss sampling constants for dominating sets in Bergman spaces. Our method is based on a Remez-type inequality by Andrievskii and Ruscheweyh. We also comment on extensions of the method to other spaces such as Fock and Paley-Wiener spaces.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
