Abstract
A notion of frame-like wavelet systems is introduced and analyzed. Those systems are not dual wavelet frames although preserve important properties of frames. The construction of such systems is based on the matrix extension principle (MEP), but it is simpler than the construction of wavelet frames.
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Averbuch, A.Z., Zheludev, V.A., Cohen, T.: Interpolatory frames in signal space. IEEE Trans. Sig. Proc. 54(6), 2126–2139 (2006)
Han, B., Shen, Z.: Dual wavelet frames and Riesz bases in Sobolev spaces. Constr. Approx. 29, 369–406 (2009)
Ehler, M.: The multiresolution structure of pairs of dual wavelet frames for a pair of Sobolev spaces. Jaen J. Approx. 2(2), 193–214 (2010)
Vladimirov, V.S.: Generalized Functions in Mathematical Physics. MIR (1979). (Translated from Russian)
Gel’fand, I.M. Ramanujan, M.S., Shilov G.E.: Generalized functions. Volume 1. Prop. Oper. Amer. Math. Monthly 74(8), 1026 (1967)
Ron, A., Shen, Z.: Compactly supported tight affine spline frames in \({L_2(R^d)}\). Math. Comp. 67, 191–207 (1998)
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Krivoshein, A., Protasov, V., Skopina, M. (2016). Frame-Like Wavelet Expansions. In: Multivariate Wavelet Frames. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-10-3205-9_4
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DOI: https://doi.org/10.1007/978-981-10-3205-9_4
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