Multiresolution and wavelets
Copyright policy )Multiresolution and wavelets
Multiresolution is investigated on the basis of shift-invariant spaces. Given a finitely generated shift-invariant subspaceSofL2(ℝd), letSkbe the 2k-dilate ofS(k∈ℤ). A necessary and sufficient condition is given for the sequence {Sk}k∈ℤto fom a multiresolution ofL2(ℝd). A general construction of orthogonal wavelets is given, but such wavelets might not have certain desirable properties. With the aid of the general theory of vector fields on spheres, it is demonstrated that the intrinsic properties of the scaling function must be used in constructing orthogonal wavelets with a certain decay rate. When the scaling function is skew-symmetric about some point, orthogonal wavelets and prewavelets are constructed in such a way that they possess certain attractive properties. Several examples are provided to illustrate the general theory.
- University of Wisconsin System United States
- University of Wisconsin–Madison United States
- University of Wisconsin–Oshkosh United States
- University of Alberta Canada
Invariant subspaces of linear operators, multiresolution, orthogonal wavelets, prewavelets, Multidimensional problems, Nontrigonometric harmonic analysis involving wavelets and other special systems, shift-invariant spaces, Approximation by other special function classes, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Invariant subspaces of linear operators, multiresolution, orthogonal wavelets, prewavelets, Multidimensional problems, Nontrigonometric harmonic analysis involving wavelets and other special systems, shift-invariant spaces, Approximation by other special function classes, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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