On completeness of root vectors of Schrodinger operators: a spectral approach

We study complete properties of root vectors of Schrdinger operators. More accurately, denote by (B(r_0) be the ball centered at the origin with radius (r_0 and (L^1(B(r_0)) the space which consists of real functions f(x) satisfying int_{B(r_0)}|f(x)|dx ∞ , then the complete properties of eigenvectors for Schrodinger equation are characterized. Our characterization depends on the sum of eigenvalues. Our proof is based on a complexanalytic conjugate approach which is widely used in the investigation of completeness of function systems in Banach spaces.