具有周期和反周期边界条件的非自伴Schrodinger算子的Schauder和Riesz基判别法
A Schauder and Riesz Basis Criterion for Non-Self-Adjoint Schrödinger Operators with Periodic and Antiperiodic Boundary Conditions
摘要：
在假设$V \in L^2([0,π]; dx)$的条件下，我们得到了在具有周期和反周期边界条件的$L^2([0,π]; dx)$中的（非自伴）薛定谔算子$-d^2/dx^2+V$具有根向量的Riesz基的充要条件（即，本征向量和广义本征向量跨越与对应的周期和反周期本征值相关联的Riesz投影的范围）。我们还讨论了周期和反周期薛定谔算子$-d^2/dx^2+V$在$L^p([0,π]; dx)$，$p \in (1,\infty)$的Schauder基础的情况。
英文摘要：
Under the assumption that $V \in L^2([0,π]; dx)$, we derive necessary and sufficient conditions for (non-self-adjoint) Schrödinger operators $-d^2/dx^2+V$ in $L^2([0,π]; dx)$ with periodic and antiperiodic boundary conditions to possess a Riesz basis of root vectors (i.e., eigenvectors and generalized eigenvectors spanning the range of the Riesz projection associated with the corresponding periodic and antiperiodic eigenvalues). We also discuss the case of a Schauder basis for periodic and antiperiodic Schrödinger operators $-d^2/dx^2+V$ in $L^p([0,π]; dx)$, $p \in (1,\infty)$.
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