On Linear Independence of Integer Translates of Refinable Vectors
نویسندگان
چکیده
منابع مشابه
Linear Independence of the Integer Translates of Compactly Supported Distributions and Reenable Vectors
Some necessary and suucient conditions in time domain for the global and local linear independence of the integer translates of compactly supported distributions and reenable vectors are established in this paper.
متن کاملLocal Linear Independence of Refinable Vectors of Functions
This paper is devoted to a study of local linear independence of refinable vectors of functions. A vector of functions φ = (φ1, . . . , φr) ∈ (C(IR))r is said to be refinable if it satisfies the vector refinement equation φ(x) = ∑ α∈Z s a(α)φ(2x− α), where a is a finitely supported sequence of r×r matrices called the refinement mask. A complete characterization for the local linear independence...
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We investigate linear independence of integer translates of a finite number of compactly supported functions in two cases. In the first case there are no restrictions on the coefficients that may occur in dependence relations. In the second case the coefficient sequences are restricted to be in some ` space (1 ≤ p ≤ ∞) and we are interested in bounding their `-norms in terms of the L-norm of th...
متن کاملLinear 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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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1998
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5858