Equiconvergence, with trigonometric series, of expansions in root functions of a one-dimensional Schrödinger operator with a complex potential in the class \(L_ 1\). (English. Russian original) Zbl 0779.34065
Differ. Equations 27, No. 4, 401-416 (1991); translation from Differ. Uravn. 27, No. 4, 577-597 (1991).
The author considers the one-dimensional non-self-adjoint Schrödinger operator
\(L\psi=-d^ 2\psi/dx^ 2+U(x)\psi\) with complex potential \(U(x)\) of class \(L_ 1\) and establishes necessary and sufficient conditions for the equiconvergence of the series of expansions of a function \(f(x)\) with respect to root functions and trigonometric functions.
\(L\psi=-d^ 2\psi/dx^ 2+U(x)\psi\) with complex potential \(U(x)\) of class \(L_ 1\) and establishes necessary and sufficient conditions for the equiconvergence of the series of expansions of a function \(f(x)\) with respect to root functions and trigonometric functions.
Reviewer: S.Balint (Timişoara)
MSC:
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 42A10 | Trigonometric approximation |
| 34L10 | Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators |
