Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L 2(R d)

Let {} be an orthonormal wavelet of L 2(R d) and the support of a whole of its Fourier transform be supp{^}=i=1d[Ai,Di]i=1d(Bi,Ci),AiBiCiDi. Under the weakest condition that each ^is continuous for w(di=1[Ai,Di]),a characterization of the above support of a whole is given.