Spectral estimations for Laplace operator for the discrete Heisenberg group
| dc.creator | Kokhas, K. | |
| dc.creator | Suvorov, A. | |
| dc.date | 1999-05-20 | |
| dc.date.accessioned | 2026-07-07T05:29:10Z | |
| dc.date.available | 2026-07-07T05:29:10Z | |
| dc.description | Let H be the discrete 3-dimensional Heisenberg group with the standard generators x, y, z. The element Delta of the group algebra for H of the form Delta= (x+x^{-1}+y+y^{-1})/4 is called the Laplace operator. This operator can also be defined as transition operator for random walk on the group. The spectrum of Delta in the regular representation of H is the interval [-1,1]. Let E(A), where A is a subset of [-1,1], be a family of spectral projectors for Delta and m(A)=(E(A)e, e) be the corresponding spectral measure. Here e is the characteristic function of the unit element of the group H. We estimate the value m([-1,-1+t] \cup [1-t,1]) when t tends to 0. More precisely we prove the inequality m([-1,-1+t] \cup [1-t,1]) > const t^{2+alpha} for any positive alpha. | |
| dc.description | 8 pages, AMSTEX(+amsppt) + 1 page: 2 figures in one Postscript file | |
| dc.identifier | https://arxiv.org/abs/math/9905133 | |
| dc.identifier | http://arxiv.org/abs/math/9905133 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78538 | |
| dc.subject | Spectral Theory | |
| dc.subject | Representation Theory | |
| dc.title | Spectral estimations for Laplace operator for the discrete Heisenberg group | |
| dc.type | text |