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SUMMARY:Mel Nathanson (CUNY)
DTSTART:20260917T190000Z
DTEND:20260917T200000Z
DTSTAMP:20260906T211433Z
UID:NYNTS/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYNTS/2/">B_
 h-sets and perturbations in normed vector spaces</a>\nby Mel Nathanson (CU
 NY) as part of New York Number Theory Seminar\n\n\nAbstract\nThe subset $A
  = \\{a_i:i \\in I\\}$ of a normed vector space is a $B_h$-set if every el
 ement \nof the sumset $hA$ has a unique representation as a sum of $h$ ele
 ments of $A$.  \nAn $\\varepsilon$-perturbation of $A$ is a set $A' = \\{a
 '_i:i\\in I\\}$ such that $|a'-a|<\\varepsilon$ \nfor all $i \\in I$. \nLe
 t $\\Delta_{hA} = \\inf\\{|x'-x| : x\,x' \\in hA \\text{ and } x\\neq x'\\
 }$.  \nIt is proved that if $A$ is  finite or countably infinite set with 
 $\\Delta_{hA}>0$\, \nthen there is a $B_h$-set $A'$ that is an $\\varepsil
 on$-perturbation of $A$.\n
LOCATION:https://researchseminars.org/talk/NYNTS/2/
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