Seminario di analisi matematica
ore
17:00
presso Seminario I
Let A be a discrete, unbounded, infinite set in R. Can
we find a "large" measurable set E in R which does not contain
any affine copy x + tA of A (for any in R, t > 0)?
If a(n) is a real, nonnegative sequence that does not increase ex-
ponentially, then, for any 0 <= p < 1, we construct a Lebesgue
measurable set which has measure at least p in any unit interval
and which contains no affine copy of the given sequence. We gen-
eralize this to higher dimensions and also for some "non-linear"
copies of the sequence. Our method is probabilistic.
Joint work with M. Kolountzakis (Univ. of Crete).
Current address: Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Greece