Linear independence of time-frequency translates
نویسندگان
چکیده
منابع مشابه
Linear Independence of Time-frequency Translates
Abstract. The refinement equation φ(t) = ∑N2 k=N1 ck φ(2t − k) plays a key role in wavelet theory and in subdivision schemes in approximation theory. Viewed as an expression of linear dependence among the time-scale translates |a|1/2φ(at − b) of φ ∈ L2(R), it is natural to ask if there exist similar dependencies among the time-frequency translates e2πibtf(t + a) of f ∈ L2(R). In other words, wh...
متن کاملLinear 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.
متن کاملLinear Independence of Time-frequency Translates in R
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: Proceedings of the American Mathematical Society
سال: 1996
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-96-03346-1