Wave functions, evolution equations and evolution kernels

The parton distribution functions and the meson wave functions are defined as Fourier transforms of matrix elements of (nonlocal) light-ray operators. Nonforward one-particle matrix elements of such operators lead to new distribution amplitudes describing both hadrons simultaneously. They are applied for the description of the exclusive virtual Compton scattering in the Bjorken region near forward direction and the two meson production process. The evolution equations for these distribution amplitudes follow from the renormalization group equation of the light-ray operators. Relations between different evolution kernels (especially the Altarelli-Parisi-Lipatov and the Brodksy-Lepage kernels) are derived. (orig.)