Mathematics of the USSR-Sbornik · 1977 · 48 citations · 8 references
Natural SciencesMathematicsPhysicsMathematical PhysicsQuantum MechanicsTheoretical PhysicsEigenvalue ProblemsHilbert Space FormalismOperator TheorySchrödinger EquationSpectral AnalysisSpectral TheoryAbsolutely Continuous SpectrumDilation TheoryEigenfunction ExpansionsHilbert Space RepresentationsProjectionsResolvent TheorySpectral RepresentationSpectral Theorem
The object of the present work is the imbedding of the spectral theory for the dissipative Schrodinger operator with absolutely continuous spectrum acting in the Hilbert space in the spectral theory of a model operator and the proof of the theorem on expansion in terms of eigenfunctions. The imbedding mentioned is achieved by constructing a selfadjoint dilation of the operator . In the so-called incoming spectral representation of this dilation the operator becomes the corresponding model operator. Next, a system of eigenfunctions of the dilation - the radiating eigenfunctions - is constructed. From these a canonical system of eigenfunctions for the absolutely continuous spectrum of the operator and its spectral projections are obtained by orthogonal projection onto .Bibliography: 22 titles.
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