On trigonometric series associated with separable, translation invariant subspaces of ๐ฟ^{โ}(๐บ)
On trigonometric series associated with separable, translation invariant subspaces of ๐ฟ^{โ}(๐บ)
<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denotes a compact abelian group, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Gamma"> <mml:semantics> <mml:mi mathvariant="normal">ฮ<!-- ฮ --></mml:mi> <mml:annotation encoding="application/x-tex">\Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denotes its dual. Our main result is that every non-Sidon set <inline-formula content-type="math/mathml"> <mml:math โฆ