Let L be the Hill operator or the one-dimensional Dirac operator with π-periodic potential considered on the real line R. The spectrum of L has a band-gap structure, that is, the intervals of continuous spectrum alternate with spectral gaps. The endpoints of these gaps are eigenvalues of the same di erential operator L but considered on the interval [0; π] with periodic or antiperiodic boundary conditions. In this thesis considering the Hill and the one-dimensional periodic Dirac operators, we provide precise asymptotics of the spectral gaps in case of speci c potentials that are linear combinations of two exponential terms
