Abstract.
We give a complete description of spectrum of the wavelet Galerkin operator
$$
R_{m_0 ,{\kern 1pt} m_0 } f(z) = \frac{1}
{N}\sum\limits_{w^N = z} {|m_0 |^2 (w)f(w),\quad (z \in \mathbb{T})}
$$
associated to a low-pass filter m0 and a scale N, in the Banach spaces \(C(\mathbb{T})\) and \(L^P (\mathbb{T}),{\kern 1pt} \,1 \leq p \leq \infty .\)
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Dutkay, D.E. The Spectrum of the Wavelet Galerkin Operator. Integr. equ. oper. theory 50, 477–487 (2004). https://doi.org/10.1007/s00020-003-1348-3
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DOI: https://doi.org/10.1007/s00020-003-1348-3