Holomorphic extension of representations: (I) automorphic functions
| dc.creator | Kroetz, Bernhard | |
| dc.creator | Stanton, Robert J. | |
| dc.date | 2002-10-07 | |
| dc.date | 2006-01-10 | |
| dc.date.accessioned | 2026-07-07T06:35:31Z | |
| dc.date.available | 2026-07-07T06:35:31Z | |
| dc.description | Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors of any irreducible unitary representation of G has a holomorphic extension to this domain. For the resultant holomorphic extension of K-finite matrix coefficients we obtain estimates of the singularities at the boundary, as well as majorant/minorant estimates along the boundary. We obtain L^\infty bounds on holomorphically extended automorphic functions on G/K in terms of Sobolev norms, and we use these to estimate the Fourier coefficients of combinations of automorphic functions in a number of cases, e.g. of triple products of Maass forms. | |
| dc.description | 84 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0210111 | |
| dc.identifier | http://arxiv.org/abs/math/0210111 | |
| dc.identifier | Ann. of Math. (2), Vol. 159 (2004), no. 2, 641--724 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99817 | |
| dc.subject | Representation Theory | |
| dc.subject | Number Theory | |
| dc.subject | 22E45 (Primary) 11F70 (Secondary) | |
| dc.title | Holomorphic extension of representations: (I) automorphic functions | |
| dc.type | text |