Pagina web del Prof. Invitado

PROPERTIES :•These spaces satisfyV... ⊂ V ⊂ V0⊂ V− 11⊂2•We say that L ( R)= ⊕ Wjj∈Z•Two more properties:∩V = {} 0 and = L 2 j∪V j( R)2•Any f ( x)∈ L ( R)can be written asP0V0f(x)∑ ∑j∈Zk ∈ Z...∞j jjjkψk( x ) , dk= ∫ f ( x ) ψk( x )− ∞= ddx= W ⊕ W ⊕ ...f(x)=1∑k∈Zsjkφjk2(x(wavelets form anorthonormal basis of L 2 )due to the orthonormality of the wavelets. In this expansion, functions witharbitrarily small-scale structures can be represented. But, in practice, in thecomputer there is a limit J, which depends on how fine the grid is in thenumerical scenario:( j is the scale and k is the location))+J∑⊕∑j = 1 k ∈ ZWdjkJψjk⊕(x)VJ