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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 355, Pages 199–218 (Mi znsl1708)  
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
Full-text PDF (1303 kB) Citations (2)
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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
English version:
Journal of Mathematical Sciences (New York), 2009, Volume 156, Issue 5, Pages 834–844
DOI: https://doi.org/10.1007/s10958-009-9291-8
Bibliographic databases:
UDC: 517.5
Language: Russian
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
Citation in format AMSBIB
\Bibitem{MakRab08}
\by I.~E.~Maksimenko, E.~L.~Rabkin
\paper Expansion of vectors in powers of a~matrix
\inbook Investigations on linear operators and function theory. Part~36
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 355
\pages 199--218
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1708}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 156
\issue 5
\pages 834--844
\crossref{https://doi.org/10.1007/s10958-009-9291-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65049089852}
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  • https://www.mathnet.ru/eng/znsl/v355/p199
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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