Linear independence of time-frequency shifts?
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...
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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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Linear independence of integer shifts of compactly supported functions plays an important role in approximation theory and wavelet analysis. In this note we provide a simple proof for two known characterizations of linear independence of integer shifts of a finite number of compactly supported distributions on R. By l(Z) we denote the space of all complex-valued sequences v = {v(k)}k∈Zd : Z → C...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2014
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-014-0637-z