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Search: MSC category 43A46 ( Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) )

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1. CMB 2016 (vol 59 pp. 521)

Hare, Kathryn; Ramsey, L. Thomas
The Relationship Between $\epsilon$-Kronecker Sets and Sidon Sets
A subset $E$ of a discrete abelian group is called $\epsilon $-Kronecker if all $E$-functions of modulus one can be approximated to within $\epsilon $ by characters. $E$ is called a Sidon set if all bounded $E$-functions can be interpolated by the Fourier transform of measures on the dual group. As $% \epsilon $-Kronecker sets with $\epsilon \lt 2$ possess the same arithmetic 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)

Hare, Kathryn E.
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
Categories:42B25, 43A46

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