Abstract For the operator defined by the differential operation $$ Lu=-y^{\prime \prime }+x^{-2}(\nu ^2-{1}/{4})y,$$ $$0<\nu <1 $$ , on the interval $$(0,1) $$ , we study the statements of spectral boundary value problems with general boundary conditions at the singular point $$x=0 $$ as well as the basis properties of the systems of cylinder functions arising in these problems. We find sufficient conditions on the spectral parameter under which these systems have the Bessel property in $$L_2(0,1) $$ .

中文翻译：

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圆柱函数非正交系统的贝塞尔性质

摘要 对于微分运算定义的算子 $$ Lu=-y^{\prime \prime }+x^{-2}(\nu ^2-{1}/{4})y,$$ $$0< \nu <1 $$ ，在 $$(0,1) $$ 区间上，我们研究了奇异点 $$x=0 $$ 处具有一般边界条件的谱边值问题的表述以及基性质在这些问题中产生的气缸功能系统。我们找到了这些系统在 $$L_2(0,1) $$ 中具有贝塞尔性质的谱参数的充分条件。