[en] Complete text of publication follows. Most of the states of unstable nuclei are unbound resonances and continuum states, which means that the studies of unstable nuclei are just related to the nuclear structure in the continuum energy region above the lowest threshold. The Coulomb breakup reaction using typical neutron-rich nuclei like ⁶He, ¹¹Li and ¹¹Be, is one of the interesting phenomena to see the fundamental excitation mechanism of unstable nuclei. The important point in analyzing the Coulomb breakup reaction is to investigate the response properties of unbound states excited from the ground state having an exotic structure like a neutron halo or skin. In seeing those responses, it is meaningful to extract the contributions from both resonances and continuum states in the transition strength simultaneously, which is also valuable to discuss the existence of a soft dipole resonance. For this purpose, we adopt complex scaling method (CSM) to express the many-body unbound states in the unified theoretical framework, with extending the applicability of CSM to evaluate the transition strength to the resonant and continuum states, respectively. In this report, we present our recent studies about the excitation mechanism of two halo nuclei: ¹¹Be and ⁶He with extracting the transition components to the 2- and 3-body unbound states of these nuclei in the breakup reaction. For the breakup of ¹¹Be into ¹⁰Be and neutron, we decompose the transition strength into the contributions from resonance and background continuum terms. It is unambiguously clarified that the process of direct breakup is dominant rather than that of resonance in comparison with the experimental data. For the 3-body breakup of ⁶He into ⁴He+2n, it is interesting to examine the role of 3-body unbound states and possibility of sequential decay to analyze the experimental cross section in connection with the halo structure of the ground state. Employing the 3-body model of ⁶He with CSM [4], we derive the contributions of not only the 3-body resonant states, but also those of the 2-body or 3-body continuum states in the electric multipole strengths. We evaluate the each component of them and analyse which states dominates the observed characteristic behavior of the strength distribution. In the transition, multipole dependency about the components of resonances and continuum states should be investigated in connection with the property of ground state. It leads to the interpretation of low energy enhancement in the strength, and also to the understanding of structure of ⁶He in the continuum region. For E1 transition, our result indicates that the sequential decay is important as much as the 3-body continuum. In addition to the continuum components, the effects of 2_1,2⁺ resonances are noticeable in the E2 transition. (author)