John-type theorems for generalized arithmetic progressions and iterated sumsets

• Autores: Terence Tao, Van H. Vu
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 2, 2008, págs. 428-449
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.05.002
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• Resumen

  • A classical theorem of Fritz John allows one to describe a convex body, up to constants, as an ellipsoid. In this article we establish similar descriptions for generalized (i.e. multidimensional) arithmetic progressions in terms of proper (i.e. collision-free) generalized arithmetic progressions, in both torsion-free and torsion settings. We also obtain a similar characterization of iterated sumsets in arbitrary abelian groups in terms of progressions, thus strengthening and extending recent results of Szemerédi and Vu.