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On a class of weak nonhomogeneous affine bi-frames for reducing subspaces of L 2(ℝd)

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Abstract

For refinable function-based affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame (WNABF). Under the setting of reducing subspaces of L 2(Rd), we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.

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Acknowledgements

The authors cordially thank the referees for their time and comments.

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Correspondence to Yun Zhang Li.

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Supported by the National Natural Science Foundation of China (Grant No. 11271037)

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Zhang, J.P., Li, Y.Z. On a class of weak nonhomogeneous affine bi-frames for reducing subspaces of L 2(ℝd). Acta. Math. Sin.-English Ser. 33, 1339–1351 (2017). https://doi.org/10.1007/s10114-017-6445-3

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  • DOI: https://doi.org/10.1007/s10114-017-6445-3

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