期刊
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING
卷 3, 期 3, 页码 347-359出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219691305000890
关键词
oblique projection; sampling; Riesz basis; frames
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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