Geodesic
Haar multiresolution analysis and Haar bases on the ring of rational adeles
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 158-165 
S. Evdokimov. Haar multiresolution analysis and Haar bases on the ring of rational adeles. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 158-165. http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a6/
@article{ZNSL_2012_400_a6,
     author = {S. Evdokimov},
     title = {Haar multiresolution analysis and {Haar} bases on the ring of rational adeles},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {158--165},
     year = {2012},
     volume = {400},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We construct a family of Haar multiresolution analyses in the Hilbert space $L^2(\mathbb A)$ where $\mathbb A$ is the ring of adeles over the field $\mathbb Q$ of rationals. The corresponding discrete group of translations and scaling function are respectively the group of additive translations by elements of $\mathbb Q$ embedded diagonally in $\mathbb A$ and the characteristic function of the standard fundamental domain of this group. As a consequence we come to a family of orthonormal wavelet bases in $L^2(\mathbb A)$. We observe that both the number of generating wavelet functions and the number of elementary dilations are infinite.

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