Abstract Result on the uniform, over the entire real line, equiconvergence of spectral expansions related to the self-adjoint extension of a general differential operation of any even order with coefficients from the one-dimensional Kato class, with the Fourier integral expansion is presented. The statement is based on the obtained uniform estimates for the spectral function of this operator.

中文翻译：

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高阶微分算子的谱展开在实线上均匀等收敛

摘要 给出了在整条实线上均匀等收敛谱展开的结果，该谱展开与任何偶数阶的一般微分运算的自伴随扩展有关，该运算具有来自一维 Kato 类的系数，具有傅立叶积分展开。该陈述基于获得的对该算子的谱函数的统一估计。