Suppose that has the property that any two exponentials with frequency from are orthogonal in the space , where is the unit disk. Such sets are known to be finite but it is not known if their size is uniformly bounded. We show that if there are two elements of which are distance apart then the size of is . As a consequence we improve a result of Iosevich and Jaming and show that has at most elements in any disk of radius .
Cite this article
Alex Iosevich, Mihail N. Kolountzakis, Size of orthogonal sets of exponentials for the disk. Rev. Mat. Iberoam. 29 (2013), no. 2, pp. 739–747