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Title: On the structure of self-affine convex bodies

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.
Authors:
 [1]
  1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22317915
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 8; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BIBLIOGRAPHIES; EQUATIONS; MATHEMATICAL OPERATORS