Some new Chebyshev spaces

In this note we see another circumstance where Chebyshev polynomials play a significant role. In particular, we present some new extended Chebyshev spaces that arise in the asymptotic stability of the zero solution of first order linear delay differential equations with mm commensurate delays y′(t)+∑j=0majy(t−jτ)=0 where aj,j=0,…,maj,j=0,…,m, are constants and τ>0τ>0 is constant.