کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898234 | 1631327 | 2018 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A sharp Balian-Low uncertainty principle for shift-invariant spaces
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A sharp version of the Balian-Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators {fk}k=1KâL2(Rd) are translated along a lattice to form a frame or Riesz basis for a shift-invariant space V, and if V has extra invariance by a suitable finer lattice, then one of the generators fk must satisfy â«Rd|x||fk(x)|2dx=â, namely, fkËâH1/2(Rd). Similar results are proven for frames of translates that are not Riesz bases without the assumption of extra lattice invariance. The best previously existing results in the literature give a notably weaker conclusion using the Sobolev space Hd/2+ϵ(Rd); our results provide an absolutely sharp improvement with H1/2(Rd). Our results are sharp in the sense that H1/2(Rd) cannot be replaced by Hs(Rd) for any s<1/2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied and Computational Harmonic Analysis - Volume 44, Issue 2, March 2018, Pages 294-311
Journal: Applied and Computational Harmonic Analysis - Volume 44, Issue 2, March 2018, Pages 294-311
نویسندگان
Douglas P. Hardin, Michael C. V, Alexander M. Powell,