Search: MSC category 43A46
( Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) )
1. CMB Online first
||The relationship between $\epsilon$-Kronecker sets and Sidon sets|
A subset $E$ of a discrete abelian group is called $\epsilon
all $E$-functions of modulus one can be approximated to within
by characters. $E$ is called a Sidon set if all bounded $E$-functions
interpolated by the Fourier transform of measures on the dual
group. As $%
\epsilon $-Kronecker sets with $\epsilon \lt 2$ possess the same
properties as Sidon sets, it is natural to ask if they are Sidon.
We use the
Pisier net characterization of Sidonicity to prove this is true.
Keywords:Kronecker set, Sidon set
Categories:43A46, 42A15, 42A55
2. CMB 2000 (vol 43 pp. 330)
||Maximal Operators and Cantor Sets |
We consider maximal operators in the plane, defined by Cantor sets of
directions, and show such operators are not bounded on $L^2$ if the
Cantor set has positive Hausdorff dimension.
Keywords:maximal functions, Cantor set, lacunary set