Ritz逼近理论中的正逆定理
Direct and inverse theorems in the theory of approximation by the Ritz method
摘要：
对于Hilbert空间$H$中的任意自伴算子$B$，我们给出了建立向量$x \in H$关于算子$B$的光滑度，算子$B$的指数型整向量的最佳逼近收敛到零的速度，以及$k$ -向量$x$关于算子$B$的连续模。所得结果可用于Hilbert空间中算子方程的Ritz近似解的先验估计。
英文摘要：
For an arbitrary self-adjoint operator $B$ in a Hilbert space $H$, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector $x \in H$ with respect to the operator $B$, the rate of convergence to zero of its best approximation by exponential-type entire vectors of the operator $B$, and the $k$-modulus of continuity of the vector $x$ with respect to the operator $B$. The results are used for finding a priori estimates for the Ritz approximate solutions of operator equations in a Hilbert space.
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