کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777563 | 1632924 | 2017 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the structure of the spectrum of small sets
ترجمه فارسی عنوان
در ساخت طیف مجموعه های کوچک
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کلمات کلیدی
طیف فوریه، مجموع مجموعه، دو برابر شدن،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
Let G be a finite Abelian group and A a subset of G. The spectrum of A is the set of its large Fourier coefficients. Known combinatorial results on the structure of spectrum, such as Chang's theorem, become trivial in the regime |A|=|G|α whenever αâ¤c, where câ¥1/2 is some absolute constant. On the other hand, there are statistical results, which apply only to a noticeable fraction of the elements, which give nontrivial bounds even to much smaller sets. One such theorem (due to Bourgain) goes as follows. For a noticeable fraction of pairs γ1,γ2 in the spectrum, γ1+γ2 belongs to the spectrum of the same set with a smaller threshold. Here we show that this result can be made combinatorial by restricting to a large subset. That is, we show that for any set A there exists a large subset Aâ², such that the sumset of the spectrum of Aâ² has bounded size. Our results apply to sets of size |A|=|G|α for any constant α>0, and even in some sub-constant regime.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 148, May 2017, Pages 1-14
Journal: Journal of Combinatorial Theory, Series A - Volume 148, May 2017, Pages 1-14
نویسندگان
Kaave Hosseini, Shachar Lovett,