Cauchy problem for one class of pseudodifferential systems with smooth symbols

For one class of pseudodifferential systems with smooth time-dependent symbols, we study properties of the fundamental matrix of solutions. We formulate sufficient and, for some systems, necessary conditions for the correct solvability of the Cauchy problem with generalized initial data. We also construct spaces of test and generalized functions that generalize certain classical spaces. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 4, pp. 502–524, October–December, 2006.