EIGENFUNCTION EXPANSION ASSOCIATED WITH THE ONE-DIMENSIONAL SCHRODINGER EQUATION ON SEMI-INFINITE TIME SCALE INTERVALS

被引：7
|
作者：
Huseynov, Adil [1 ]
机构：
[1] Ankara Univ, Dept Math, TR-06100 Ankara, Turkey
来源：
REPORTS ON MATHEMATICAL PHYSICS | 2010年 / 66卷 / 02期
关键词：
time scale; delta and nabla derivatives; Jacobi matrix; spectral function; FINITE;
D O I：
10.1016/S0034-4877(10)00026-1
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We prove the existence of a spectral function (spectral measure or orthogonality measure) for the one-dimensional Schrodinger 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 Schrodinger operator on the semi-axis and for semi-infinite Jacobi matrices.
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页码：207 / 235
页数：29
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