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Generalized number systems in Euclidean spaces

✍ Scribed by I. Kátai

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
569 KB
Volume
38
Category
Article
ISSN
0895-7177

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✦ Synopsis

The concept of number systems in higher-dimensional Euclidean spaces as well as in number fields are introduced and treated. The paper is mainly a survey of known results. If %k denotes the ring of integer vectorials in Euclidean space lkk then we study the subgroup C = M&,

where M is a L x k matrix with integer entries. A digit set is defined with the help of residue classes (mod C) Aj (j = 0, . , t -l), where t = 1 det MI. The analogous of q-additive and q-multiplicative functions over the ring of Gaussian integers are also given.

📜 SIMILAR VOLUMES

-Isometries in Euclidean spaces
-Isometries in Euclidean spaces
✍ Igor A. Vestfrid 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 128 KB

Let 0 < r R and A be a subset of the n-dimensional Euclidean space E n , which is contained in B(x 0 , R) and contains points x 0 , x 0 + re 1 , . . . , x 0 + re n , where the vectors {e i } n i=1 are orthonormal. We show that if f : A → E n is an -isometry, then there is an affine isometry U such t