ar X iv : 0 90 5 . 08 78 v 1 [ m at h . FA ] 6 M ay 2 00 9 Spectral Models for Orthonormal Wavelets and Multiresolution Analysis of L 2 ( R )
نویسندگان
چکیده
Spectral representations of the dilation and translation operators on L 2 (R) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes.
منابع مشابه
ar X iv : 0 80 9 . 05 00 v 1 [ m at h . FA ] 2 S ep 2 00 8 DIRECT LIMITS , MULTIRESOLUTION ANALYSES , AND WAVELETS
A multiresolution analysis for a Hilbert space realizes the Hilbert space as the direct limit of an increasing sequence of closed subspaces. In a previous paper, we showed how, conversely, direct limits could be used to construct Hilbert spaces which have multiresolution analyses with desired properties. In this paper, we use direct limits, and in particular the universal property which charact...
متن کاملar X iv : 0 90 4 . 09 09 v 1 [ m at h . FA ] 6 A pr 2 00 9 On Sobolev extension domains in R
We describe a class of Sobolev W k p -extension domains Ω ⊂ R n determined by a certain inner subhyperbolic metric in Ω. This enables us to characterize finitely connected Sobolev W 1 p -extension domains in R 2 for each p > 2 .
متن کاملar X iv : 0 90 6 . 01 60 v 1 [ m at h . FA ] 3 1 M ay 2 00 9 OPERATOR MACHINES ON DIRECTED GRAPHS PETR
We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X −→ X such that the set A = {x ∈ X : ||R(x)|| → ∞} is non-empty and nowhere dense in X . Moreover, if x ∈ X \ A then some subsequence of (R(x)) n=1 converges weakly to x. This answers in the negative a recent conjecture of Prǎjiturǎ. The result can be extended to any Ba...
متن کاملar X iv : 0 90 4 . 31 78 v 1 [ m at h . FA ] 2 1 A pr 2 00 9 TREE METRICS AND THEIR LIPSCHITZ - FREE SPACES
We compute the Lipschitz-free spaces of subsets of the real line and characterize subsets of metric trees by the fact that their Lipschitz-free space is isometric to a subspace of L1.
متن کاملar X iv : 0 90 7 . 28 62 v 1 [ m at h . FA ] 1 6 Ju l 2 00 9 On the stability of J ∗ − derivations
In this paper, we establish the stability and superstability of J∗−derivations in J∗−algebras for the generalized Jensen–type functional equation rf( x+ y r ) + rf( x− y r ) = 2f(x). Finally, we investigate the stability of J∗−derivations by using the fixed point alternative.
متن کامل