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 contribution | Some further results in analogy to a theorem of Koksma on uniform distribution |
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Original language | German |
Pages (from-to) | 203-220 |
Number of pages | 18 |
Journal | Monatshefte für Mathematik |
Volume | 92 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Sept 1981 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)