Affiliation: College of Charleston
Email: jinr@cofc.edu
Title Of Talk: Recent Results on Inverse Problems
URL: http://math.cofc.edu/jin/research/publication.html
Abstract: In the early 1960's G. Freiman revealed an interesting inverse phenomenon, which says that if A+A is small, then A must have some arithmetic structure. Let A be a set of natural numbers, finite or infinite. In the talk, the arithmetic structure of A or A+A is characterized when A+A is small in terms of each of the following conditions: (1) A is finite, |A| is large enough, and |A+A|=3|A|-3+b for some small non-negative integers b, (2) A is infinite, gcd(A-minA)=1, the upper asymptotic density of A is less than 0.5, and the upper asymptotic density of A+A is 1.5 times the upper asymptotic density of A, (3) A is infinite and the upper Banach density of A+A is less than 2 times the upper Banach density of A.
Last update made Thu Nov 11 14:46:35 EST 2004.
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