Abstract

A class of quadratic irregular pencils of the second order ordinary differential operators with constant coefficients is considered in this paper. It is assumed that the boundary conditions are splitting and the characteristic equation has positive roots. Both amounts of two-fold expansions in the series in terms of eigenfunctions of such pencils and necessary and sufficient conditions for convergence of these expansions to the decomposed vector-valued function are found. For this class of irregular pencils, the question of a two-fold expansion in terms of eigenfunctions was not considered earlier.

中文翻译：

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关于一类二阶微分算子的不规则二次铅笔的本征函数展开

摘要

本文考虑了一类具有常系数的二阶常微分算子的二次不规则铅笔。假设边界条件是分裂的，特征方程有正根。找到了就这些铅笔的本征函数而言的系列中的二重展开的数量以及这些展开收敛到分解的向量值函数的充分必要条件。对于这类不规则铅笔，之前没有考虑本征函数的二次展开问题。