Generalized Fourier representation of the absolutely continuous part of   a selfadjoint operator
  We formulate and prove the existence and uniqueness of the generalized Fourier transform associated with the absolutely continuous part of an arbitrary selfadjoint operator on a separable Hilbert space. To this end we develop a novel method to decompose an absolutely continuous operator into a variable fiber direct integral of selfadjoint operators. 
Take-Yuki Nagao
math.FA math-ph math.MP math.SP