GLOBAL REPRESENTATIONS OF THE HEAT AND SCHRODINGER EQUATION WITH SINGULAR POTENTIAL

被引：0
作者：
Franco, Jose A. [1 ]
Sepanski, Mark R. [2 ]
机构：
[1] Univ N Florida, Jacksonville, FL 32082 USA
[2] Baylor Univ, Waco, TX 76798 USA
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年
关键词：
Schrodinger equation; heat equation; singular potential; Lie theory; representation theory; globalization;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The n-dimensional Schrodinger equation with a singular potential V-lambda(x) = lambda parallel to x parallel to(-2) is studied. Its solution space is studied as a global representation of S<(L(2,R))over tilde> x O(n). A special subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. The space of K-finite vectors is calculated, obtaining conditions for lambda so that this space is non-empty. The direct sum of solution spaces over such admissible values of lambda is studied as a representation of the 2n + 1-dimensional Heisenberg group.
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页数：16
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