On the asymptotic distribution of the powers of S × S -matrices

V. Losert; W.-G. Nowak; R. F. Tichy

Compositio Mathematica (1982)

  • Volume: 45, Issue: 2, page 273-291
  • ISSN: 0010-437X

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Losert, V., Nowak, W.-G., and Tichy, R. F.. "On the asymptotic distribution of the powers of $S \times S$-matrices." Compositio Mathematica 45.2 (1982): 273-291. <http://eudml.org/doc/89536>.

@article{Losert1982,
author = {Losert, V., Nowak, W.-G., Tichy, R. F.},
journal = {Compositio Mathematica},
keywords = {asymptotic distribution; sequence of powers of real matrix; discrepancy},
language = {eng},
number = {2},
pages = {273-291},
publisher = {Martinus Nijhoff Publishers},
title = {On the asymptotic distribution of the powers of $S \times S$-matrices},
url = {http://eudml.org/doc/89536},
volume = {45},
year = {1982},
}

TY - JOUR
AU - Losert, V.
AU - Nowak, W.-G.
AU - Tichy, R. F.
TI - On the asymptotic distribution of the powers of $S \times S$-matrices
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 45
IS - 2
SP - 273
EP - 291
LA - eng
KW - asymptotic distribution; sequence of powers of real matrix; discrepancy
UR - http://eudml.org/doc/89536
ER -

References

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  1. [1] J. Dieudonné, Grundzüge der modernen Analysis III, Vieweg, Braunschweig, 1976. Zbl0341.58002MR349287
  2. [2] P. Erdös and J.F. Koksma, On the uniform distribution mod 1 of lacunary sequences, Indag. Math.11 (1949), 79-88. Zbl0033.16502MR30556
  3. [3] P. Erdös and J.F. Koksma, On the uniform distribution mod 1 of sequences (f(n, δ)), Indag. Math.11 (1949), 299-302. Zbl0035.32101
  4. [4] I.S. Gal et J.F. Koksma, Sur l'ordre de grandeur des fonctions sommables, C.R. Acad. d. Sc. Paris277 (1948), 1321-1323. Zbl0041.02404MR27353
  5. [5] P. Gerl, Einige metrische Sätze in der Theorie der Gleichverteilung modulo 1, Journal f.d. reine u. ang. Math.216 (1964), 50-66. Zbl0135.10902MR162772
  6. [6] E. Hlawka, Theorie der Gleichverteilung, Mannheim- Wien-Zürich, B.I., 1979. Zbl0406.10001MR542905
  7. [7] J.F. Koksma, Ein mengentheoretischer Satz über die Gleichverteilung modulo Eins, Compositio Math.2 (1935), 250-258. Zbl0012.01401JFM61.0205.01
  8. [8] L. Kuipers and H. Niederreiter, Uniform distribution of sequences, New York, John Wiley and Sons, 1974. Zbl0281.10001MR419394
  9. [9] C.G. Lekkerkerker, Geometry of numbers, North-Holland-Publ.-Comp., Amsterdam, 1969. Zbl0198.38002MR271032
  10. [10] W.J. Leveque, The distribution mod 1 of trigonometric sequences, Duke Math. Journal20 (1963), 367-374. Zbl0051.28504MR57925
  11. [11] W.G. Nowak, Zur Gleichverteilung mod 1 der Potenzen von Quaternionen mit Norm größer als 1, Archiv d. Math.34 (1980), 243-248. Zbl0418.10048MR590315
  12. [12] W.G. Nowak und R.F. Tichy, Über die Verteilung mod 1 der Potenzen reeller (2 x 2)-Matrizen, Indag. Math., accepted for publication. Zbl0452.10046
  13. [13] W.G. Nowak und R.F. Tichy, Einige weitere Resultate in Analogie Zu einem Gleichverteilungssatz von Koksma, Monatsh. f. Math., accepted for publication. Zbl0459.10033
  14. [14] V.G. Sprindžuk, Metric theory of diophantine approximation, (engl. transl.), Scripta series in mathematics, Winston and sons, Washington D.C., 1979. MR548467
  15. [15] R.F. Tichy, Ein Analogon zum Satz von Koksma in Quaternionen, Archiv d. Math, 32 (1979), 346-348. Zbl0401.10060MR545157

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