For refinable functiombased 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 funct...For refinable functiombased 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 L2（Rd）, we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11271037)
文摘For refinable functiombased 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 L2（Rd）, we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.
