Internal structure of the multiresolution analyses defined by the unitary extension principle

Cited 2 time in webofscience Cited 0 time in scopus
  • Hit : 458
  • Download : 0
We analyze the internal structure of the multiresolution analyses of L(2)(R(d)) defined by the unitary extension principle (UEP) of Ron and Shen. Suppose we have a wavelet tight frame defined by the UEP. Define V(0) to be the closed linear span of the shifts of the scaling function and W(0) that of the shifts of the wavelets. Finally, define V(1) to be the dyadic dilation of V(0). We characterize the,conditions that V(1) = W(0), that V(1) = V(0) <(+)over dot> W(0) and V(1) = V(0) circle plus W(0). In particular, we show that if we construct a wavelet frame of L(2)(R) from the UEP by using two trigonometric filters, then V(1) = V(0) <(+)over dot>+ W(0); and show that V(1) = W(0) for the B-spline example of Ron and Shen. A more detailed analysis of the various 'wavelet spaces' defined by the B-spline example of Roil and Shen is also included. (C) 2008 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2008
Language
English
Article Type
Article
Keywords

SHIFT-INVARIANT SPACES; COMPACTLY SUPPORTED TIGHT; AFFINE SYSTEMS; FRAMES; L-2(R-D); WAVELETS; L(2)(R(D))

Citation

JOURNAL OF APPROXIMATION THEORY, v.154, no.2, pp.140 - 160

ISSN
0021-9045
DOI
10.1016/j.jat.2008.03.009
URI
http://hdl.handle.net/10203/88659
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 2 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0