Ambarzumyan-type theorem for third order linear measure differential equations

This paper deals with the Ambarzumyan-type theorem for a complex third order linear measure differential equation idy & PRIME;& BULL;+2iqxy & PRIME;dx+yidqx+dpx=lambda ydx on [0, 1] with boundary conditions y1=0, y & PRIME;1=y & PRIME;0, and hy(0)+y & PRIME;& BULL;0=0, where p & ISIN;M(I,R), q & ISIN;M0(I,R), and h=-h. More precisely, we prove that if the eigenvalues of this boundary value problem are (2n pi)(3), n = 0, & PLUSMN;1, & PLUSMN;2, horizontal ellipsis , then h = 0 and the measure coefficients p(x) = p(0), q(x) = 0 for x & ISIN; [0, 1).