论文标题
在高阶线性差方程的最佳ULAM常数上
On the best Ulam constant of a higher order linear difference equation
论文作者
论文摘要
在Banach Space $ x $中，线性差异方程式具有恒定系数$ x_ {n +p} = a_1x_ {n +p-1} +\ ldots +a_px_n，$仅当roots $ r_k，$ r_k，$ r_k，$ r_k，$ $ 1 \ leq k \ leq p，$ leq k \ leq p，$属于其特征等式的circial do do nity do nity do nity nity nity do nity nity circip.如果$ | r_k | > 1，$ 1 \ $ 1 \ leq k \ leq p，$我们证明，该方程的最佳ULAM常数为$ \ frac {1} {| V |} \ sum \ limits_ {s = 1}^{\ infty} | \ frac {v_1} {r_1^s} - \ frac {v_2} {v_2} {r_2^s}}}}}}}+\ ldots +\ frac {（ - 1）^{p+1} v_p} {r_p^s} |，$ where $ v = v = v（r_1，r_2，r_2，\ ldots，r_p）$和$ v_k = v（r_1，r_1，\ ldots，\ ldots，\ ldots，r_ {k-1}，r_ {k-1}，r_ {k-1}，r_ { k \ leq p，$是vadermonde的决定因素。
In a Banach space $X$ the linear difference equation with constant coefficients $x_{n+p} = a_1x_{n+p-1} +\ldots + a_px_n,$ is Ulam stable if and only if the roots $r_k,$ $1\leq k\leq p,$ of its characteristic equation do not belong to the unit circle. If $|r_k| > 1,$ $1\leq k\leq p,$ we prove that the best Ulam constant of this equation is $ \frac{1}{|V|}\sum\limits_{s=1}^{\infty}|\frac{V_1}{r_1^s}-\frac{V_2}{r_2^s}+\ldots +\frac{(-1)^{p+1}V_p}{r_p^s}|,$ where $ V = V (r_1, r_2, \ldots, r_p)$ and $V_k =V (r_1,\ldots, r_{k-1}, r_{k+1},\ldots, r_p),$ $1\leq k\leq p,$ are Vadermonde determinants.
