ON THE EIGENFUNCTIONS OF THE MONODROMY OPERATOR OF THE SCHRÖDINGER OPERATOR WITH A TIME-PERIODIC POTENTIAL
ON THE EIGENFUNCTIONS OF THE MONODROMY OPERATOR OF THE SCHRÖDINGER OPERATOR WITH A TIME-PERIODIC POTENTIAL
复制标题
论具有时间周期势的薛定谔算子的单调算子的本征函数
DOI：
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发表时间：
1985
期刊：
影响因子：
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通讯作者：
E. Korotyaev
中科院分区：
文献类型：
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作者：
E. Korotyaev
证明了具有时间周期势和空间变量快速减少势的Schrodinger算子的单值算子的本征函数在空间变量中衰减的速度比任何幂都快，并研究了单值算子的谱.证明了：1）monodromy算子没有奇异连续谱; 2）monodromy算子的特征函数总数（计重数）是有限的。
It is shown that the eigenfunctions of the monodromy operator of the Schrodinger operator (with a potential periodic in time and rapidly decreasing in the space variables) decay in the space variables faster than any power.The spectrum of the monodromy operator is also investigated. It is proved that 1) the monodromy operator has no singular continuous spectrum; and 2) the total number of eigenfunctions of the monodromy operator (counting multiplicity) is finite.Bibliography: 19 titles.