Daubechies' time-frequency localization operator on Cantor type sets II

نویسندگان

چکیده

We study a version of the fractal uncertainty principle in joint time-frequency representation. Namely, we consider Daubechies' localization operator projecting onto spherically symmetric n-iterate Cantor sets with an arbitrary base M>1 and alphabet A. derive upper bound asymptote up to multiplicative constant for norm terms M size |A| set. For any fixed size, show that there are such is optimal. In particular, precise mid-third set, which was studied part I [19]. Nonetheless, this does not extend every set as provide examples where optimal achieved.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Equilibrium Cantor-type Sets

Equilibrium Cantor-type sets are suggested. This allows to obtain Green functions with various moduli of continuity and compact sets with preassigned growth of Markov’s factors.

متن کامل

Daubechies Localization Operator in Bargmann - Fock Space and Generating Function of Eigenvalues of Localization Operator

We will express Daubechies localization operators in Bargmann Fock space. We will prove that the Hermite functions are eigenfunctions of Daubechies localization operator. By making use of generating function of eigenvalues of Daubechies localization operator, we will show some reconstruction formulas for symbol function of Daubechies localization operator with rotational invariant symbol.

متن کامل

Dimensions of subsets of cantor-type sets

Let I = [0,1] be the unit interval on the real line andm> 1 be an integer. Let J = {0,1, . . . , m− 1}. For every point x ∈ I , there is a unique base-m representation x = Σk=1 jkm−k with jk ∈ J except for countable many points. Since countable sets do not interfere with our work, we neglect them here. For each j ∈ J , x ∈ [0,1], and n ∈ N, let τj(x,n) = {k : ik = j, 1 ≤ k ≤ n}, then the limit ...

متن کامل

Cantor sets

This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω of irrationals, or certain of its subspaces. In particular, given f ∈ (ω\{0}), we consider compact sets of the form Q i∈ω Bi, where |Bi| = f(i) for all, or for infinitely many, i. We also consider “n-splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω, |{g(i) : ...

متن کامل

Two measures on Cantor sets

We give an example of Cantor-type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous. Also we show that these two measures are regular in the Stahl–Totik sense. c ⃝ 2014 Elsevier Inc. All rights reserved. MSC: 30C85; 31A15; 28A78; 28A80

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Functional Analysis

سال: 2022

ISSN: ['0022-1236', '1096-0783']

DOI: https://doi.org/10.1016/j.jfa.2022.109412