Support theorem for the fundamental solution to the Schrodinger equation on certain compact symmetric spaces
Support theorem for the fundamental solution to the Schrodinger equation on certain compact symmetric spaces
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某些紧对称空间上薛定谔方程基本解的支持定理
DOI：
10.1016/j.aim.2010.10.003
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
T.Kakehi
中科院分区：
文献类型：
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作者：
Seiya Negami;J. Mada and T. Tokihiro;Atsushi Atsuji;Y.Ohta and J.Yang;Y. Takei;利根川吉廣;T.Kakehi
本文利用Heckman和Opam的移位算子，构造了具有偶根重数的紧对称空间上薛定谔方程的基本解。其次，我们证明了基本解的支撑点在有理时刻成为低维的子集，而它的支撑点和奇点支撑点在无理时刻与整个对称空间重合。此外，我们还证明了在基本解的表达式中出现了广义高斯和。
In this paper we construct the fundamental solution to the Schödinger equation on a compact symmetric space with even root multiplicities using shift operators of Heckman and Opdam. Next, we prove that the support of the fundamental solution becomes a lower dimensional subset at a rational time whereas its support and its singular support coincide with the whole symmetric space at an irrational time. Moreover, we also show that generalized Gauss sums appear in the expression of the fundamental solution.