标题： 无反射算子和自守Herglotz函数 显示英文标题

标题： Reflectionless operators and automorphic Herglotz functions

摘要： 我对在开集上为反射无的规范系统和狄拉克算子感兴趣。在这种情况下，半直线$m$函数是彼此的解析延拓，可以组合成一个单一函数。通过将其定义域的万有覆盖空间，我们得到这些算子与相对于覆盖变换的富克斯群为自守的赫尔维茨函数之间的一一对应关系。我研究这种形式主义的性质，特别关注在相应意义上自守的测度。这将有助于理解反射无算子作为拓扑空间、其极值点，以及如何将广泛研究的有限间隙算子的较小空间置于（大得多的）空间中。 显示英文摘要

摘要： I am interested in canonical systems and Dirac operators that are reflectionless on an open set. In this situation, the half line $m$ functions are holomorphic continuations of each other and may be combined into a single function. By passing to the universal cover of its domain, we then obtain a one-to-one correspondence of these operators with Herglotz functions that are automorphic with respect to the Fuchsian group of covering transformations. I investigate the properties of this formalism, with particular emphasis given to the measures that are automorphic in a corresponding sense. This will shed light on the reflectionless operators as a topological space, on their extreme points, and on how the heavily studied smaller space of finite gap operators sits inside the (much) larger space.