On linear independence of integer shifts of compactly supported distributions
نویسندگان
چکیده
منابع مشابه
On linear independence of integer shifts of compactly supported distributions
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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Given a multivariate compactly supported distribution φ, we derive here a necessary and sufficient condition for the global linear independence of its integer translates. This condition is based on the location of the zeros of φ̂ = The Fourier-Laplace transform of φ. The utility of the condition is demonstrated by several examples and applications, showing in particular, that previous results on...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2016
ISSN: 0021-9045
DOI: 10.1016/j.jat.2015.08.008