A Remark on Spectral Properties of Certain Non-selfadjoint Schrodinger Operators

作者：Aiba Daisuke^*

来源：Tokyo Journal of Mathematics, 2013, 36(2): 337-345.

In this paper, we study the spectral and pseudospectral properties of the differential operator H-epsilon = -partial derivative(2)(x) + x(2m) + i epsilon(-1) f(x) on L-2(R), where epsilon > 0 is a small parameter, m is an element of N and f is a real-valued Morse function which satisfies vertical bar partial derivative(l)(x)(f(x) - vertical bar x vertical bar(-k)) <= C vertical bar x vertical bar(-k-l-1) for l = 0, 1, 2, 3 and large vertical bar x vertical bar. We show that Psi(epsilon) = (sup(lambda is an element of R) parallel to (H-epsilon - i lambda)(-1) parallel to)(-1) and Sigma(epsilon) = infR(sigma(H-epsilon)) satisfy C-1 epsilon(-v(m)) <= Psi (epsilon) <= C epsilon(-v(m)) and Sigma(epsilon) >= C-1 epsilon(-v(m)), v(m) = min {2m/k+3m+1, 1/2}. This extends the result of I. Gallagher, T. Gallay and F. Nier [3] (2009) for the case m = 1 to general m is an element of N.

• 出版日期2013-12