2021/09/14 by Baias, Alina-Ramona, Popa, Dorian
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2109.06833
The linear differential operator with constant coefficients D(y)=y(n)+a1 y(n-1)+…+an y, y∈ Cn(ℝ, X) acting in a Banach space X is Ulam stable if and only if its characteristic equation has no roots on the imaginary axis. We prove that if the characteristic equation of D has distinct roots rk satisfying \Real rk>0, 1≤ k≤ n, then the best Ulam constant of D is KD=(1)/(|V|)∫0∞|∑k=1n(-1)kVke-rk x|dx, where V=V(r1,r2,…,rn) and Vk=V(r1,…,rk-1,rk+1, …, rn), 1≤ k≤ n, are Vandermonde determinants.