Lax-Phillips散射算子的行列式
The determinant of the Lax-Phillips scattering operator
摘要：
设$M$表示有限体积、不含椭圆点的非紧黎曼曲面，$B$表示Lax-Phillips散射算子。使用由于Voros的superzeta函数方法，我们定义了一个Hurwitz型zeta函数$ζ^{\pm}_{B}(s,z)$构造从相关的共振$zI -[ (1/2)I \pm B]$。证明了$ζ^{\pm}_{B}(s,z)$在$s$中的亚纯延拓，并利用$s=0$中的特殊值，定义了算子$zI -[ (1/2)I \pm B]$的行列式.我们获得的塞尔伯格的zeta函数和行列式的散射矩阵的运营商决定因素方面的表达式。
英文摘要：
Let $M$ denote a finite volume, non-compact Riemann surface without elliptic points, and let $B$ denote the Lax-Phillips scattering operator. Using the superzeta function approach due to Voros, we define a Hurwitz-type zeta function $ζ^{\pm}_{B}(s,z)$ constructed from the resonances associated to $zI -[ (1/2)I \pm B]$. We prove the meromorphic continuation in $s$ of $ζ^{\pm}_{B}(s,z)$ and, using the special value at $s=0$, define a determinant of the operators $zI -[ (1/2)I \pm B]$. We obtain expressions for Selberg's zeta function and the determinant of the scattering matrix in terms of the operator determinants.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
