Hyperbolic systems in Gelfand and Shilov spaces

Abstract

UDC 517.956.32, 517.955.2
For systems hyperbolic in Shilov's sense with time-dependent coefficients, the properties of the Green function are studied in the $S$-type spaces. For systems of this kind in the indicated spaces, we establish the correct solvability of the Cauchy problem. It is shown that, for each $\beta>1,$ the space ${S_0^\beta}'$ of Gelfand and Shilov distributions is the class of well-posedness of this problem.