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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 400, Pages 158–165
(Mi znsl5615)
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This article is cited in 7 scientific papers (total in 7 papers)
Haar multiresolution analysis and Haar bases on the ring of rational adeles
S. Evdokimov St. Petersburg Department of the Steklov Mathematical
Institute, St. Petersburg, Russia
Abstract:
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.
Key words and phrases:
ring of adeles, multiresolution analysis, Haar bases, generating wavelet function.
Received: 26.03.2012
Citation:
S. Evdokimov, “Haar multiresolution analysis and Haar bases on the ring of rational adeles”, Problems in the theory of representations of algebras and groups. Part 23, Zap. Nauchn. Sem. POMI, 400, POMI, St. Petersburg, 2012, 158–165; J. Math. Sci. (N. Y.), 192:2 (2013), 215–219
Linking options:
https://www.mathnet.ru/eng/znsl5615 https://www.mathnet.ru/eng/znsl/v400/p158
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Abstract page: | 372 | Full-text PDF : | 69 | References: | 48 |
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