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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 355, Pages 199–218
(Mi znsl1708)
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This article is cited in 2 scientific papers (total in 2 papers)
Expansion of vectors in powers of a matrix
I. E. Maksimenkoa, E. L. Rabkinb a St. Petersburg State University of Information Technologies, Mechanics and Optics
b St. Petersburg State University of Telecommunications
Abstract:
In this paper, we investigate the problem of expansion of any $d$-dimensional vector in powers of a dilation matrix $M$. (A dilation matrix is an integral matrix of size $d\times d$ with all eigenvalues greater than 1 in modulus.) This expansion can be viewed as a multidimensional system of numeration with the matrix as the base and a special set of vectors as the set of digits. We give a constructive method of expanding an integral vector in powers of a dilation matrix and prove the existence of an expansion for any real vector. Bibl. – 4 titles.
Received: 31.03.2008
Citation:
I. E. Maksimenko, E. L. Rabkin, “Expansion of vectors in powers of a matrix”, Investigations on linear operators and function theory. Part 36, Zap. Nauchn. Sem. POMI, 355, POMI, St. Petersburg, 2008, 199–218; J. Math. Sci. (N. Y.), 156:5 (2009), 834–844
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https://www.mathnet.ru/eng/znsl1708 https://www.mathnet.ru/eng/znsl/v355/p199
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Abstract page: | 310 | Full-text PDF : | 147 | References: | 37 |
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