具有边界控制的Hermite heat equation的可达空间
Reachable space of the Hermite heat equation with boundary control
摘要：
讨论了具有边界$L^2$ -控制的线段上Hermite热方程的可达态.埃尔米特热方程对应于热方程，其中二次势被添加。我们将讨论两种情况：当线段的一个端点是原点时，以及当线段相对于原点对称时。其中一个主要结果是，可达状态扩展到函数在伯格曼空间的一个正方形的对角线是所考虑的部分，和功能全纯在附近的这个广场是可达的。
英文摘要：
We discuss reachable states for the Hermite heat equation on a segment with boundary $L^2$-controls. The Hermite heat equation corresponds to the heat equation to which a quadratic potential is added. We will discuss two situations: when one endpoint of the segment is the origin and when the segment is symmetric with respect to the origin. One of the main results is that reachable states extend to functions in a Bergman space on a square one diagonal of which is the segment under consideration, and that functions holomorphic in a neighborhood of this square are reachable.
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