Under study is the multidimensional inverse problem of determining the convolutional kernel of the integral term in an integro-differential wave equation. The direct problem is represented by a generalized initial-boundary value problem for this equation with zero initial data and the Neumann boundary condition in the form of the Dirac delta-function. For solving the inverse problem, the traces of the solution to the direct problem on the domain boundary are given as an additional condition. The main result of the article is the theorem of global unique solvability of the inverse problem in the class of functions continuous in the time variable \( t \) and analytic in the space variable. We apply the methods of scales of Banach spaces of real analytic functions of variable and weight norms in the class of continuous functions.

正在研究确定积分微分波动方程中积分项的卷积核的多维逆问题。直接问题由具有零初始数据和Dirac三角函数形式的Neumann边界条件的该方程的广义初边界值问题表示。为了解决反问题，在域边界上给出了直接问题解的迹线作为附加条件。本文的主要结果是在时间变量\（t \）中连续的函数类中的反问题的全局唯一可解性定理 并在空间变量中进行分析。在连续函数的一类中，我们应用了变量和权范数的实解析函数的Banach空间的尺度方法。