TY - JOUR
AU - V. A. Litovchenko
PY - 2019/10/25
Y2 - 2023/09/30
TI - Hyperbolic systems in Gelfand and Shilov spaces
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 71
IS - 10
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1520
AB - 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.
ER -