We consider the boundary value problems (BVPs) for linear secondorder ODEs with a strongly positive operator coefficient in a Banach space. The solutions are given in the form of the infinite series by means of the Cayley transform of the operator, the Meixner type polynomials of the independent variable, the operator Green function and the Fourier series representation for the right-hand side of the equation. The approximate solution of each problem is a partial sum of N (or expressed through N) summands. We prove the weighted error estimates depending on the discretization parameter N, the distance of the independent variable to the boundary points of the interval and some smoothness properties of the input data.

中文翻译：

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Banach空间中边值问题的凯莱变换方法的加权估计

我们考虑 Banach 空间中具有强正算子系数的线性二阶 ODE 的边界值问题 (BVP)。通过算子的凯莱变换、自变量的梅克斯纳型多项式、算子格林函数和方程右侧的傅立叶级数表示，以无穷级数的形式给出解。每个问题的近似解是 N 个（或通过 N 个）被加数的部分和。我们证明了加权误差估计取决于离散化参数 N、自变量到区间边界点的距离以及输入数据的一些平滑特性。