Abstract

In this paper we study a spectral problem with spectral parameter in the boundary condition. This problem arises when solving boundary value problems for mixed type equations using the spectral method. We analyze the system of root functions of this problem and proof two theorems about basis properties of this system. The biortogonal system is constructed and uniform convergence of spectral expansions is studied.

中文翻译：

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边界条件下带谱参数问题的根函数系统的基本性质

摘要

在本文中，我们研究了在边界条件下具有光谱参数的光谱问题。当使用频谱方法求解混合型方程的边值问题时，会出现此问题。我们分析了该问题的根函数系统，并证明了有关该系统基本性质的两个定理。构建了生物正交系统，研究了谱扩展的均匀收敛。