The Munich Near-Infrared Cluster Survey -: V.: The evolution of the rest-frame K- 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 deg(2) in the near-infrared K ' and J passbands, and 0.35 deg(2) in I , R , V , and, recently completed, B . The spectroscopic sample comprises observations of objects down to a limit of K 'less than or equal to 17.5 in five survey fields (0.17 deg(2) in total), and a sparsely selected deeper sample (K 'less than or equal to 19.0) constructed in one of the survey patches (0.03 deg(2) ). 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 such as 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, 0.4 and 0.7. We find evidence for mild evolution of magnitudes (DeltaM * (K) similar or equal to-0.70 mag) and number densities (DeltaPhi* (K) /Phi* (K) similar or equal to-0.35) to a redshift of unity. 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.