论文标题
通过其光谱数据重建高阶差异操作员
Reconstruction of higher-order differential operators by their spectral data
论文作者
论文摘要
本文涉及高阶（$ n> 2 $）普通差分运算符的逆频谱问题。我们从光谱数据中为具有规则或分布系数的各种差分运算符开发了重建方法。我们的方法是基于将反向问题减少到有界无限序列Banach空间中线性方程的基础。该方程以通用形式得出，可以应用于各种差分运算符类别。也证明了线性主方程的独特可溶性。通过使用主方程的解决方案，我们以串联形式得出了差分表达系数的重建公式，并证明了几类运算符的这些系列的收敛性。本文的结果可用于逆光谱问题的建设性解决方案，并研究其解决性和稳定性。
This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either regular or distribution coefficients. Our approach is based on the reduction of an inverse problem to a linear equation in the Banach space of bounded infinite sequences. This equation is derived in a general form that can be applied to various classes of differential operators. The unique solvability of the linear main equation is also proved. By using the solution of the main equation, we derive reconstruction formulas for the differential expression coefficients in the form of series and prove the convergence of these series for several classes of operators. The results of this paper can be used for constructive solution of inverse spectral problems and for investigation of their solvability and stability.
