کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607978 1337894 2009 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Density results for Gabor systems associated with periodic subsets of the real line
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Density results for Gabor systems associated with periodic subsets of the real line
چکیده انگلیسی

The well-known density theorem for one-dimensional Gabor systems of the form {e2πimbxg(x−na)}m,n∈Z, where g∈L2(R)g∈L2(R), states that a necessary and sufficient condition for the existence of such a system whose linear span is dense in L2(R)L2(R), or which forms a frame for L2(R)L2(R), is that the density condition ab≤1 is satisfied. The main goal of this paper is to study the analogous problem for Gabor systems for which the window function gg vanishes outside a periodic set S⊂RS⊂R which is aZ-shift invariant. We obtain measure-theoretic conditions that are necessary and sufficient for the existence of a window gg such that the linear span of the corresponding Gabor system is dense in L2(S)L2(S). Moreover, we show that if this density condition holds, there exists, in fact, a measurable set E⊂RE⊂R with the property that the Gabor system associated with the same parameters a,ba,b and the window g=χEg=χE, forms a tight frame for L2(S)L2(S).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 157, Issue 2, April 2009, Pages 172–192
نویسندگان
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