منابع مشابه
Introduction to Hilbert Space Frames
We present an introduction to Hilbert space frames. A frame is a generalization of a basis that is useful, for example, in signal processing. It allows us to expand Hilbert space vectors in terms of a set of other vectors that satisfy a certain “energy equivalence” condition. This condition guarantees that any vector in the Hilbert space can be reconstructed in a numerically stable way from its...
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We develope a local theory for frames on finite dimensional Hilbert spaces. We show that for every frame (fi) m i=1 for an n-dimensional Hilbert space, and for every ǫ > 0, there is a subset I ⊂ {1, 2, . . . ,m} with |I| ≥ (1 − ǫ)n so that (fi)i∈I is a Riesz basis for its span with Riesz basis constant a function of ǫ, the frame bounds, and (‖fi‖) m i=1 , but independent of m and n. We also con...
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In this paper, we establish some new results in ultra Bessel sequences and ultra Bessel sequences of subspaces. Also, we investigate ultra Bessel sequences in direct sums of Hilbert spaces. <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-s...
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We prove that any tight frame in Hilbert space can be obtained by the Kaczmarz algorithm. An explicit way of constructing this correspondence is given. The uniqueness of the correspondence is determined.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2008.10.040