Parametrix and asymptotics of the spectral function of differential operators in $\mathbf R^n$

A new formula is obtained for a global parametrix of the Cauchy problem for hyperbolic equations and systems which is an analogue of the representation of the Green function in terms of the spectral function of the corresponding steady-state operator. In the selfadjoint case this formula makes it possible to obtain a complete asymptotic expansion of the spectral function of elliptic operators in $\mathbf R^n$.
Bibliography: 18 titles.