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.

引用

页码：207 / 235

页数：29

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