Continuity of the Joint Spectral Radius: Application to Wavelets
نویسندگان
چکیده
Abstract. The joint spectral radius is the extension to two or more matrices of the (ordinary) spectral radius ρ(A) = max |λi(A)| = lim‖A m‖1/m. The extension allows matrix products Πm taken in all orders, so that norms and eigenvalues are difficult to estimate. We show that the limiting process does yield a continuous function of the original matrices—this is their joint spectral radius. Then we describe the construction of wavelets from a dilation equation with coefficients ck. We connect the continuity of those wavelets to the value of the joint spectral radius of two matrices whose entries are formed from the ck.
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