Linear independence of time frequency translates for special configurations
نویسندگان
چکیده
منابع مشابه
Linear Independence of Time Frequency Translates for Special Configurations
We prove that for any 4 points in the plane that belong to 2 parallel lines, there is no linear dependence between the associated time-frequency translates of any nontrivial Schwartz function. If mild Diophantine properties are satisfied, we also prove linear independence in the category of L2(R) functions.
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We establish the linear independence of time-frequency translates for functions f on R having one sided decay limx∈H, |x|→∞ |f(x)|ec|x| log |x| = 0 for all c > 0, which do not vanish on an affine half-space H ⊂ R.
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We establish the linear independence of time-frequency translates for functions f having one sided decay limx→∞ |f(x)|e log x = 0 for all c > 0. We also prove such results for functions with faster than exponential decay, i.e., limx→∞ |f(x)|e = 0 for all c > 0, under some additional restrictions.
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2010
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2010.v17.n4.a14