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CATEGORIES:Analysis seminar
SUMMARY:Explicit Salem Sets in R^n - Rob Fraser (Edinburgh
)
DTSTART:20200121T140000Z
DTEND:20200121T150000Z
UID:TALK4073AT
URL:/talk/index/4073
DESCRIPTION:In 1981\, R. Kaufman showed that the $\\tau$-appro
ximable numbers in $\\mathbb{R}$ support a measure
$\\mu$ satisfying \n\n$\n|\\hat{\\mu}|\\leq C_\\e
psilon (1+|\\xi|)^\n-1/(1+\\tau)+\\epsilon\n$ \n\n
for any $\\epsilon>0$. The exponent $-1/(1+\\tau)$
is optimal for a set with Hausdorff dimension $2/
(1+\\tau)$. Sets supporting a measure with nearly
optimal pointwise Fourier decay for their Hausdorf
f dimension are called Salem sets. We show that a
higher-dimensional analogue of the $\\tau$-approxi
mable numbers is a Salem set. This provides the fi
rst explicit example of a Salem set of dimension o
ther than 0\, n-1\, or n in $\\mathbb{R}^n$. (Join
t work with Kyle Hambrook)\n
LOCATION:WATN-R17 18\, Watson Building
CONTACT:Hong Duong
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