Uncertainty Principle on Compact Extensions of the Heisenberg Group
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let G = K Hn be a compact extension of the Heisenberg group, where K is a compact subgroup of U(n) acting on the Heisenberg group Hn = Cn × R by automorphisms. We formulate and prove an analogue of Hardy’s theorem on G using ”reducible” representations. We also formulate analogues of Hardy’s theorem and Miyachi's theorem on G in terms of heat kernels. In the same context, conditions leading to the uniqueness of solutions to the Schr¨odinger problem are given.
Abstract
Let G = K Hn be a compact extension of the Heisenberg group, where K is a compact subgroup of U(n) acting on the Heisenberg group Hn = Cn × R by automorphisms. We formulate and prove an analogue of Hardy’s theorem on G using ”reducible” representations. We also formulate analogues of Hardy’s theorem and Miyachi's theorem on G in terms of heat kernels. In the same context, conditions leading to the uniqueness of solutions to the Schr¨odinger problem are given.