Size of orthogonal sets of exponentials for the disk

  • Alex Iosevich

    University of Rochester, USA
  • Mihail N. Kolountzakis

    University of Crete, Iraklio, Greece


Suppose that ΛR2\Lambda \subseteq \mathbb{R}^2 has the property that any two exponentials with frequency from Λ\Lambda are orthogonal in the space L2(D)L^2(D), where DR2D \subseteq \mathbb{R}^2 is the unit disk. Such sets Λ\Lambda 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 Λ\Lambda which are distance tt apart then the size of Λ\Lambda is O(t)O(t). As a consequence we improve a result of Iosevich and Jaming and show that Λ\Lambda has at most O(R2/3)O(R^{2/3}) elements in any disk of radius RR.

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

DOI 10.4171/RMI/737