The spectrum of the wavelet Galerkin operator

Dorin Ervin Dutkay

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The spectrum of the wavelet Galerkin operator

Dorin Ervin Dutkay

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Abstract

We give a complete description of spectrum of the wavelet Galerkin operator $$R_{m_0,m_0}f(z)=\frac{1}{N}\sum_{w^N=z}|m_0|^2(w)f(w),\quad(z\in\m athbb{T})$$ associated to a a low-pass filter $m_0$ and a scale $N$, in the Banach spaces $C(\mathbb{T})$ and $L^{p}(\mathbb{T})$, $1\leq p\leq\infty$.

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Dorin Ervin Dutkay. 2005-11-05. The spectrum of the wavelet Galerkin operator. https://arxiv.org/abs/math/0511136

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