کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8904455 1633704 2017 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Decay rate of Fourier transforms of some self-similar measures
ترجمه فارسی عنوان
میزان کاهش تبدیل فوریه برخی از اقدامات خودپسندیده
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی
This paper is concerned with the Diophantine properties of the sequence {ξθn}, where 1≤ξ<θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μλ with λ=θ-1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μλ almost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Acta Mathematica Scientia - Volume 37, Issue 6, November 2017, Pages 1607-1618
نویسندگان
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