Bessel sequences,wavelet frames,duals and extensions |
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Authors: | TC Easwaran Nambudiri K Parthasarathy |
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Institution: | 1. Department of Mathematics, Government Brennen College, Dharmadam, Thalassery, Kerala 670106, India;2. Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India |
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Abstract: | From the perspectives of duality and extensions, Gabor frames and wavelet frames have contrasting behaviour. Our chief concern here is about duality. Canonical duals of wavelet frames may not be wavelet frames, whereas canonical duals of Gabor frames are Gabor frames. Keeping these in view, we give several constructions of wavelet frames with wavelet canonical duals. For this, a simple characterisation of Bessel sequences and a general commutativity result are given, the former also leading naturally to some extension results. |
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Keywords: | Bessel sequence Frame Canonical dual Frame operator Gabor frame Wavelet frame |
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