The Relationship Between $\epsilon$-Kronecker Sets and Sidon Sets
Printed: Sep 2016
L. Thomas Ramsey,
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.
Kronecker set, Sidon set
43A46 - Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
42A15 - Trigonometric interpolation
42A55 - Lacunary series of trigonometric and other functions; Riesz products