Construction of wavelets with multiplicity
نویسنده
چکیده
Riassunto: Sia X un sottoinsieme di r elementi di uno spazio di Hilbert H e sia V0 il sottospazio chiuso generato dall’iterazione di X mediante l’operatore unitario U = (U1, . . . , Ud). Analogamente sia V1 ⊃ V0 il sottospazio generato da un insieme Y con s > r elementi. Si descrivono alcuni metodi per costruire un insieme Γ con s − r elementi che generi in modo simile il complemento ortogonale di V0 in V1. Come caso particolare si considerano H = L(IRd), U f = f(. − n) e V1 = {f(A.) : f ∈ V0} per una matrice A di interi. Le costruzioni sono illustrate con alcuni esempi dove V0 è uno spazio di splines di grado arbitrario su di una griglia a 4 direzioni in IR
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