If ψ \psi generates an affine frame ψ j , k ( x ) = 2 j / 2 ψ ( 2 j x − k ) , j , k ∈ Z {\psi _{j,k}}(x) = {2^{j/2}}\psi ({2^j}x - k),j,k \in \mathbb {Z} , of L 2 ( R ) {L^2}(\mathbb {R}) , we prove that { n − 1 / 2 ψ j , k / n } \{ {n^{ - 1/2}}{\psi _{j,k/n}}\} is also an affine frame of L 2 ( R ) {L^2}(\mathbb {R}) with the same frame bounds for any positive odd integer n . This establishes the result stated as the title of this paper. A counterexample of this statement for n = 2 n = 2 is also given.
CITATION STYLE
Chui, C. K., & Shi, X. L. (1994). 𝑛× oversampling preserves any tight affine frame for odd 𝑛. Proceedings of the American Mathematical Society, 121(2), 511–517. https://doi.org/10.1090/s0002-9939-1994-1182699-5
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