Affine dual frames and Extension Principles
نویسندگان
چکیده
منابع مشابه
Extension Principles for Dual Multiwavelet Frames of L2(r) Constructed from Multirefinable Generators
In this work we prove that any pair of homogeneous dual multiwavelet frames of L2(R) constructed from a pair of refinable function vectors gives rise to a pair of nonhomogeneous dual multiwavelet frames and vice versa. We also prove that the Mixed Oblique Extension Principle characterizes dual multiwavelet frames. Our results extend recent characterizations of affine dual frames derived from sc...
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Since the extension principles of constructing wavelet frames were presented, a lot of symmetric and compactly supported wavelet frames with high vanishing moments have been constructed. However the problem of constructing periodic wavelet frames with the help of extension principles is open. In this paper, we will construct tight periodic wavelet frames using the unitary extension principle an...
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A unitary extension principle for constructing normalized tight wavelet frames of periodic functions of one or higher dimensions is established. While the wavelets are nonstationary, the method much simplifies their construction by reducing it to a matrix extension problem that involves finite rows of complex numbers. Further flexibility is achieved by reformulating the result as an oblique ext...
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In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2014
ISSN: 1063-5203
DOI: 10.1016/j.acha.2013.02.003