Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn uniform distribution of $alphabeta$-orbits
51
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Let $alpha, beta in (0,1)$ such that at least one of them is irrational. We take a random walk on the real line such that the choice of $alpha$ and $beta$ has equal probability $1/2$. We prove that almost surely the $alphabeta$-orbit is uniformly distributed module one, and the exponential sums along its orbit has the square root cancellation. We also show that the exceptional set in the probability space, which does not have the property of uniform distribution modulo one, is large in the terms of topology and Hausdorff dimension.
rate research
Read More
Applying the theory of elliptic functions we establish two Jacobi theta function identities. From these identities we confirm two q-trigonometric identities conjectured by Gosper. As an application, we give a new and simple proof of a Pi_{q}-identity of Gosper.
We prove that quasiconvex functions always admit descent trajectories bypassing all non-minimizing critical points.
In this paper, we prove a structure theorem for the infinite union of $n$-adic doubling measures via techniques which involve far numbers. Our approach extends the results of Wu in 1998, and as a by product, we also prove a classification result related to normal numbers.
We establish $L^ptimes L^q$ to $L^r$ estimates for some paraproducts, which arise in the study of the bilinear Hilbert transform along curves.
Using the wavelet theory introduced by the author and J. Benedetto, we present examples of wavelets on p-adic fields and other locally compact abelian groups with compact open subgroups. We observe that in this setting, the Haar and Shannon wavelets (which are at opposite extremes over the real numbers) coincide and are localized both in time and in frequency. We also study the behavior of the translation operators required in the theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
