We prove that there exist necessary conditions on a weighted wavelet system with finitely many generators in order that it possesses frame bounds. Specifically, we prove that if such a system possesses an upper frame bound, then the upper weighted affine density is finite. Further, under some hypotheses, we prove that if such a system possesses a lower frame bound, then the lower affine density is strictly positive.
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Qualitative Density Conditions. In: Affine Density in Wavelet Analysis. Lecture Notes in Mathematics, vol 1914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72949-5_4
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DOI: https://doi.org/10.1007/978-3-540-72949-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72916-7
Online ISBN: 978-3-540-72949-5
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