Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1899458 | Reports on Mathematical Physics | 2010 | 29 Pages |
Abstract
We prove the existence of a spectral function (spectral measure or orthogonality measure) for the one-dimensional Schrödinger equation on semi-infinite time scale intervals. A Parseval equality and an expansion formula in eigenfunctions are established in terms of the spectral function. The result obtained unifies and extends the well-known results on the existence of a spectral measure for the one-dimensional Schrödinger operator on the semi-axis and for semi-infinite Jacobi matrices.
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