Journal
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING
Volume 3, Issue 3, Pages 347-359Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219691305000890
Keywords
oblique projection; sampling; Riesz basis; frames
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We introduce a general framework for consistent linear reconstruction in infinite-dimensional Hilbert spaces. We study stable reconstructions in terms of Riesz bases and frames, and generalize the notion of oblique dual frames to infinte-dimensional frames. As we show, the linear reconstruction scheme coincides with the so-called oblique projection, which turns into an ordinary orthogonal projection when adapting the inner product. The inner product of interest is, in general, not unique. We characterize the inner products and the corresponding positive operators for which this geometrical interpretation applies.
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