The Munich Near-Infrared Cluster Survey (MUNICS) - V. The evolution of the rest-frame K-band and J-band galaxy luminosity functions to z ~ 0.7

We present spectroscopic follow-up observations of galaxies from the Munich Near-Infrared Cluster Survey (MUNICS). MUNICS is a wide-field medium-deep K'-band selected survey covering 1 square degree in the near-infrared K' and J pass-bands, and 0.35 square degrees in I, R, V, and - recently completed - B. The spectroscopic sample comprises observations of objects down to a limit of K' < 17.5 in five survey fields (0.17 square degrees in total), and a sparsely selected deeper sample (K' < 19.0) constructed in one of the survey patches (0.03 square degrees). Here we describe the selection procedure of objects for spectroscopic observations, the observations themselves, the data reduction, and the construction of the spectroscopic catalogue containing roughly 500 galaxies with secure redshifts. Furthermore we discuss global properties of the sample like its distribution in colour-redshift space, the accuracy of redshift determination, and the completeness function of the data. We derive the rest-frame K'-band luminosity function of galaxies at median redshifts of z = 0.2, z = 0.4, and z = 0.7. We find evidence for mild evolution of magnitudes (-0.70 mag) and number densities (35 per cent) to redshift one. Furthermore, we present the rest-frame J-band luminosity function of galaxies at these redshifts, the first determination of this quantity at higher redshifts, with a behaviour similar to the K-band luminosity function.