منابع مشابه
Linear Independence of Parseval Wavelets
We establish several results yielding linear independence of the affine system generated by ψ in exchange for conditions on the space V (ψ) of negative dilates. A typical assumption yielding linear independence is that the space V (ψ) is shift-invariant. In particular, the affine system generated by a Parseval wavelet is linearly independent. As an illustration of our techniques, we give an alt...
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We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...
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New ideas were introduced in [3] to treat the problem of connectivity of Parseval frames. With these ideas it was shown that a large set of Parseval frames is arcwise connected. In this article we exhibit a larger class of Parseval frames for which the arcwise connectivity is true. This larger class fails to include all Parseval frames.
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Abstract. A composite dilation Parseval frame wavelet is a collection of functions generating a Parseval frame for L2(Rn) under the actions of translations from a full rank lattice and dilations by products of elements of groups A and B. A minimally supported frequency composite dilation Parseval frame wavelet has generating functions whose Fourier transforms are characteristic functions of set...
متن کاملLinear Independence of Characters
Example 1.1. A field homomorphism K → F is a character by restricting it to the nonzero elements of K (that is, using G = K×) and ignoring the additive aspect of a field homomorphism. In particular, when L/K is a field extension any element of Aut(L/K) is a field homomorphism L→ L and therefore is a character of L× with values in L×. Example 1.2. For any α ∈ F×, the map Z→ F× by k 7→ αk is a ch...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2010
ISSN: 0019-2082
DOI: 10.1215/ijm/1318598681