正压原始方程的谱和初值问题的解I：＝常数

本文运用Ｌａｐｌａｃｅ变换法和围道积分法分析线性化的正压原始方程组的谱问题。通过严格的数学推演从形式上给出了方程组的初值问题的解，从而原则上决定了连续谱、离散谱的出现条件。与已有的研究结果相比较，本文最大的特点是保证了了解的完备性，因而相应的展开定理便是自然的了。

The Spectrum of the System of the Barotropic Primitive Equations and its Solution with Initial Values Part I: =const

In this paper the methods of Laplace transform and residue integration are used analyse the spectrum of the system of linearized barotropic primitive equations. From explicit reduction of mathematics, the solution to the initial value problem is obtained, (U=const.), thus the conditions of the appearance of continuous spectrum and discrete spectrum are determined in principal. Compared with earlier results, an apparent feature of this paper is the completeness of the solution, and hence the expansion theorem is naturally valid.