The paper presents an experimental and theoretical study of the radiative emission in the pure krypton lamp excited by dielectric barrier discharge. Parametric studies were made in the aim to observe the influence of the applied voltage, the gas pressure and the frequency on the radiation intensity emission from visible to infrared range. Stable dielectric barrier discharges were achieved between two identical insulated electrodes separated by 2mm gap containing pure krypton at pressure from 129 to 460mbar. The discharge was powered with a sinusoidal supply at frequencies from 10 to 50kHz. Electrical characteristics of the DBD were studied. A spectroscopic and kinetic analysis of a pure krypton dielectric barrier discharge is reported here. The discharge emits radiations in UV, visible and IR range. In order to understand the emission process a theoretical interpretation of the results is given in the IR range by describing the chemical properties of the lamp. IR emission and a detailed study of kinetics allow to follow the population of metastable excited states of Krypton in (Kr*(P-3(0,2))). This population is indirectly responsible for UV emission.