Perron-Frobenius operators and the Klein-Gordon equation
  We study the non-uniqueness sets for solutions to the Klein-Gordon equation in 1 space dimension, for solutions whose Fourier transform is a finite complex measure absolutely continuous with respect to arc length. We show that generally, in the non-unique case for lattice-crosses, the space of solutions that vanish there is infinite-dimensional. 
Francisco Canto-Martin, Haakan Hedenmalm, Alfonso Montes-Rodriguez
math.DS math.AP math.FA