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Size of orthogonal sets of exponentials for the disk

Size of orthogonal sets of exponentials for the disk

Suppose that \Lambda \subseteq \mathbb{R}^2 has the property that any two exponentials with frequency from \Lambda are orthogonal in the space L^2(D) , where D \subseteq \mathbb{R}^2 is the unit disk. Such sets \Lambda are known to be finite but it is not known if their size is uniformly bounded. …