论文标题
在第二学期中具有运算符函数的抽象演化方程
Abstract evolution equations with an operator function in the second term
论文作者
论文摘要
在本文中，在Abel-Lidskii Sense中引入了一系列的汇聚，我们为进化方程提出了宝贵的应用。本文的主要问题是一种方法，使我们主要扩大了在抽象希尔伯特空间中进化方程的右侧施加的条件。 通过这种方式，我们得出了无界非频道操作员功能的定义。同时，考虑到主要问题，我们涉及一个附加概念，该概念是对非频谱操作员的光谱定理的概括。
In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations. The main issue of the paper is an approach allowing us to principally broaden conditions imposed upon the right-hand side of the evolution equation in the abstract Hilbert space. In this way, we come to the definition of the function of an unbounded non-selfadjoint operator. Meanwhile, considering the main issue we involve an additional concept that is a generalization of the spectral theorem for a non-selfadjoint operator.
