"An application of Krein Reproducing Kernel Modules"
Cerejeiras, PaulaMany applications linked to ultrahyperbolic equations and underlying noncommutative structures such as the spherical X-ray transform require function spaces associated to indefinite inner products. In this situation Hilbert modules are not the right choice as they do not reflect the induced geometry and so-called Clifford-Krein modules appear as a natural answer. Even more, one needs the equivalent of Hilbert spaces with reproducing kernels. Here we are going discuss the theory of Clifford-Krein modules with reproducing kernels and present examples of its use like in the crystallographic X-ray transform and for ultrahyperbolic Dirac operators. This is a Joint work with U. Kaehler.