کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4589721 1334902 2016 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Density and duality theorems for regular Gabor frames
ترجمه فارسی عنوان
تراشکاری و قضیه دوگانگی برای فریم های منظم گابور
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We investigate Gabor frames on locally compact abelian groups with time–frequency shifts along non-separable, closed subgroups of the phase space. Density theorems in Gabor analysis state necessary conditions for a Gabor system to be a frame or a Riesz basis, formulated only in terms of the index subgroup. In the classical results the subgroup is assumed to be discrete. We prove density theorems for general closed subgroups of the phase space, where the necessary conditions are given in terms of the “size” of the subgroup. From these density results we are able to extend the classical Wexler–Raz biorthogonal relations and the duality principle in Gabor analysis to Gabor systems with time–frequency shifts along non-separable, closed subgroups of the phase space. Even in the euclidean setting, our results are new.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 270, Issue 1, 1 January 2016, Pages 229–263
نویسندگان
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