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- W2355273359 abstract "In this paper,we summarize the properties of multiresolution analysis and analyse the essential properties of multiresolution analysis,and then we give the simplest definition of multiresolution analysis.Namely,let {V_j}_(j∈z) be a sequence of closed subspace in L~2(R),if it satisfies the following conditions:(1)monotonicity:…V_(-1)V_0V_1V_2…;(2)density:((∪)+∞j=-∞V_j)=L~2(R);(3)scalability:f(x)∈V_jf(2x)∈V_(j+1),j∈Z;(4)existence of Riesz basis:(x)∈V_0,such that {(x-k):k∈Z} is a Riesz basis of V_0,then we call {V_j}_(j∈z) a mulitiresolution analysis in L~2(R)." @default.
- W2355273359 created "2016-06-24" @default.
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- W2355273359 date "2006-01-01" @default.
- W2355273359 modified "2023-09-26" @default.
- W2355273359 title "On the Definition of Multiresolution Analysis" @default.
- W2355273359 hasPublicationYear "2006" @default.
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