Hyperbolic systems in Gelfand and Shilov spaces - Litovchenko, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2026)
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 β>1, the space S_0^β’ of Gelfand and Shilov distributions is the class of well-posedness of this problem.