常系数线性微分算符的最佳 Ulam 常数
经典分析与常微分方程
2021-09-15 v1
摘要
常系数线性微分算符 D ( y ) = y ( n ) + a 1 y ( n − 1 ) + … + a n y , y ∈ C n ( R , X ) D(y)=y^{(n)}+a_1 y^{(n-1)}+\ldots+a_n y,\quad y\in \mathcal{C}^{n}(\mathbb{R}, X) D ( y ) = y ( n ) + a 1 y ( n − 1 ) + … + a n y , y ∈ C n ( R , X ) X X X D D D r k r_k r k \Real r k > 0 , \Real r_k>0, \Real r k > 0 , 1 ≤ k ≤ n , 1\leq k\le n, 1 ≤ k ≤ n , D D D K D = 1 ∣ V ∣ ∫ 0 ∞ ∣ ∑ k = 1 n ( − 1 ) k V k e − r k x ∣ d x , K_D=\frac{1}{|V|}\int_{0}^{\infty}\left|\sum\limits_{k=1}^n(-1)^kV_ke^{-r_k x}\right|dx, K D = ∣ V ∣ 1 ∫ 0 ∞ k = 1 ∑ n ( − 1 ) k V k e − r k x d x , V = V ( r 1 , r 2 , … , r n ) V=V(r_1,r_2,\ldots,r_n) V = V ( r 1 , r 2 , … , r n ) V k = V ( r 1 , … , r k − 1 , r k + 1 , … , r n ) , V_k=V(r_1,\ldots,r_{k-1},r_{k+1}, \ldots, r_n), V k = V ( r 1 , … , r k − 1 , r k + 1 , … , r n ) , 1 ≤ k ≤ n , 1\leq k\leq n, 1 ≤ k ≤ n ,
引用
@article{arxiv.2109.06833,
title = {On the best Ulam constant of the linear differential operator with constant coefficients},
author = {Alina-Ramona Baias and Dorian Popa},
journal= {arXiv preprint arXiv:2109.06833},
year = {2021}
}