On the structure of self-affine convex bodies
Journal Article
·
· Sbornik. Mathematics
- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
We study the structure of convex bodies in R{sup d} that can be represented as a union of their affine images with no common interior points. Such bodies are called self-affine. Vallet's conjecture on the structure of self-affine bodies was proved for d = 2 by Richter in 2011. In the present paper we disprove the conjecture for all d≥3 and derive a detailed description of self-affine bodies in R{sup 3}. Also we consider the relation between properties of self-affine bodies and functional equations with a contraction of an argument. Bibliography: 10 titles.
- OSTI ID:
- 22317915
- Journal Information:
- Sbornik. Mathematics, Vol. 204, Issue 8; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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