Some remarks about polynomials which are orthogonal with respect to an indefinite weight
Some remarks about polynomials which are orthogonal with respect to an indefinite weight
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关于与不定权重正交的多项式的一些评论
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
A. Schneider
中科院分区：
文献类型：
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作者：
H. Langer;A. Schneider
本文考虑了关于不定权函数的Laguerre-， Legendre-和jacobi型正交多项式（见[LK]）。在[LK]中，一些参数的值被排除，因为在这些情况下，相应的Pontrjagin空间中相关算子的特征向量不形成一个完整的系统。结果表明，在这些特殊情况下，出现了代数上的非简单特征值，为了得到一个完整的系统，特征函数系统必须被那些非特征函数的根函数增广。
In this note Laguerre-, Legendre- and Jacobi-type orthogonal polynomials with respect to an indefinite weight function are considered (see [LK]). In [LK] some values of the parameters are excluded, as in these cases the eigenvectors of the associated operators in the corresponding Pontrjagin spaces do not form a complete system. It is shown, that in these exceptional cases algebraically nonsimple eigenvalues appear, and in order to get a complete system, the system of eigenfunctions has to be augmented by those root functions, which are not eigenfunctions.