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Abstract <p>In a half-space, for hyperbolic equations with translation operators in lower-order derivatives acting in all coordinate directions, a multiparameter family of solutions is constructed in explicit form using integral transforms. A theorem is proved stating that the obtained solutions are classical provided that the real part of the symbol of the differential-difference operator is positive.</p>

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Classical Solutions of Hyperbolic Equations in a Half-Space with a Translation Operator in Lower-Order Derivatives

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • N. V. Zaitseva

摘要

Abstract

In a half-space, for hyperbolic equations with translation operators in lower-order derivatives acting in all coordinate directions, a multiparameter family of solutions is constructed in explicit form using integral transforms. A theorem is proved stating that the obtained solutions are classical provided that the real part of the symbol of the differential-difference operator is positive.