Abstract

Marcel Riesz has created a new method to solve non-homogeneous linear equations, generalizing the fractional Riemann–Liouville integral. We generalize and apply this method to solve linear equations with Bessel operators acting with respect to all variables. This method includes the overcoming of difficulties of the theory of differential equations, caused by the occurrence of divergent integrals. Namely, in some cases (for example, for hyperbolic equations), it is necessary to use the analytical continuation of a potential analytically depending on a parameter.

中文翻译：

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双曲Riesz B势和迭代的非齐次B双曲方程的解

摘要

马塞尔·里斯（Marcel Riesz）创建了一种求解非齐次线性方程组的新方法，将分数Riemann-Liouville积分泛化。我们将这种方法推广并应用到贝塞尔算子对所有变量起作用的线性方程组中。该方法克服了由于发散积分的出现而引起的微分方程理论的难题。即，在某些情况下（例如，对于双曲方程），有必要根据参数解析地使用势的解析连续性。