横向Laplace算子的二次型的推广
Extensions of the quadratic form of the transverse Laplace operator
摘要：
本文讨论了空间坐标系中作用于向量函数横截分量的Laplace算子的二次型。作用于角动量为1和2的横向分量之一的参数化函数上的算子似乎是具有亏指数（1，1）的四阶对称微分算子。我们开发这些运营商的自伴扩展，并提出相应的扩展初始二次型。角动量2的相关标积不同于矢量函数空间中的原始乘积，但它仍然是径向变量的局部。
英文摘要：
We review the quadratic form of the Laplace operator in 3 dimensions in spehrical coordinates which acts on the transverse components of vector functions. Operators, acting on the parametrizing functions of one of the transverse components with angular momentum 1 and 2, appear to be fourth order symmetric differential operators with deficiency indices (1,1). We develop self-adjoint extensions of these operators and propose correspondent extensions for the initial quadratic form. The relevant scalar product for the angular momentum 2 differs from the original product in the space of vector functions, but nevertheless it is still local in radial variable.
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