Einige weitere Resultate in Analogie zu einem Gleichverteilungssatz von Koksma

Translated title of the contribution: Some further results in analogy to a theorem of Koksma on uniform distribution

Werner Georg Nowak*, Robert F. Tichy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Continuing former investigations by the authors (see the references) the present paper contains metric results on the distribution modulo 1 of the powers of special kinds of real matrices A, namely of (2×2)- and (3×3)-triangle matrices, symmetric (2×2)-matrices and so-called "cosymmetric" (2×2)-matrices (i. e. matrices, symmetric with respect to the secondary diagonal). For almost all such matrices A (in the sense of the Lebesgue measure in ℝ3 resp. ℝ6) possessing no eigenvalue of modulus smaller than 1 the inequality {Mathematical expression} is proved as an estimate for the discrepancy of the sequence (As(n)) where (s(n))n=1/∞ is an arbitrary fixed strictly increasing sequence of positive integers and d is the dimension of the appropriate space ℝd (d=3 or 6).

Translated title of the contributionSome further results in analogy to a theorem of Koksma on uniform distribution
Original languageGerman
Pages (from-to)203-220
Number of pages18
JournalMonatshefte für Mathematik
Volume92
Issue number3
DOIs
Publication statusPublished - 1 Sep 1981
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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