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 \( {S}_0^{\beta \prime } \) of Gelfand and Shilov distributions from the class of well-posedness of this problem.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 10, pp. 1360–1373, October, 2019.
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Litovchenko, V.A. Hyperbolic Systems in Gelfand and Shilov Spaces. Ukr Math J 71, 1555–1571 (2020). https://doi.org/10.1007/s11253-020-01731-y
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DOI: https://doi.org/10.1007/s11253-020-01731-y