For systems hyperbolic in Shilov’s sense whose coefficients are continuous functions of time, we study the properties of the Green function in S -type spaces. For systems of this kind in the indicated spaces, we prove that the Cauchy problem is correctly solvable. It is shown that, for any β > 1 , the space S 0 β ′ $$ {S}_0^{\beta \prime } $$ of Gelfand and Shilov distributions from the class of well-posedness of this problem.

中文翻译：

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Gelfand 和 Shilov 空间中的双曲系统

对于希洛夫意义上的双曲系统，其系数是时间的连续函数，我们研究了 S 型空间中格林函数的性质。对于指定空间中的此类系统，我们证明柯西问题是正确可解的。结果表明，对于任何 β > 1 ，来自该问题适定性类的 Gelfand 和 Shilov 分布的空间 S 0 β ′ $$ {S}_0^{\beta \prime } $$。