论文标题
关于Herglotz-Nevanlinna在物质科学中的应用，I：总和规则的经典理论和应用
On applications of Herglotz-Nevanlinna functions in material sciences, I: classical theory and applications of sum rules
论文作者
论文摘要
这是评论文章的第一部分，该文章着重于Herglotz-Nevanlinna在物质科学中的作用。它从标量的定义开始，重视HERGLOTZ-NEVANLINNA函数，并详细解释了与应用相关的定理，然后简要概述了这些功能的矩阵值和运算符值和运算符值，以及从标量案例中带来的属性。该理论与与总和规则相关的电磁学的某些应用补充。 Herglotz Nevanlinnna在材料科学中的更多应用可以在第二部分中找到。
This is the first part of the review article which focuses on theory and applications of Herglotz-Nevanlinna functions in material sciences. It starts with the definition of scalar valued Herglotz-Nevanlinna functions and explains in detail the theorems that are pertinent to applications, followed by a short overview of the matrix-valued and operator-valued versions of these functions and the properties that carry over from scalar cases. The theory is complemented by some applications from electromagnetics that are related to the sum rules. More applications of Herglotz Nevanlinnna functions in material sciences can be found in Part II.
