Bounded and Exponentially Decreasing in time Solutions to High-Order Hyperbolic Equations

The paper is a continuation of [7] and devoted to high-order hyperbolic operators whose symbols have no zeros in a strip δ_-< lm$\tau$ <δ₊, where $\tau$ is the variable duel to the time variable t. Two types of results are presented. In the case δ₊ = +\infty (or δ_- = -\infty ) for the corresponding operator we prove the unique solvability of the Cauchy problem on the semiaxis ±t ≥ 0 in the spaces of functions decreasing exponentially as t → ±\infty . In the case of finite δ_± the unique solvability on the whole time axis in the spaces of bounded in t functions is proved. The results of this paper are based on the estimates are obtained in [7].