Some new observations on interpolation in the spectral unit ball
| dc.creator | Bharali, Gautam | |
| dc.date | 2007-04-16 | |
| dc.date | 2007-09-17 | |
| dc.date.accessioned | 2026-07-07T09:20:21Z | |
| dc.date.available | 2026-07-07T09:20:21Z | |
| dc.description | We present several results associated to a holomorphic-interpolation problem for the spectral unit ball Ω_n, n\geq 2. We begin by showing that a known necessary condition for the existence of a $\mathcal{O}(D;Ω_n)$-interpolant (D here being the unit disc in the complex plane), given that the matricial data are non-derogatory, is not sufficient. We provide next a new necessary condition for the solvability of the two-point interpolation problem -- one which is not restricted only to non-derogatory data, and which incorporates the Jordan structure of the prescribed data. We then use some of the ideas used in deducing the latter result to prove a Schwarz-type lemma for holomorphic self-maps of Ω_n, n\geq 2. | |
| dc.description | Added a definition (Def.1.1); 2 of the 4 results herein are minor refinements of those in the author's preprint math.CV/0608177; to appear in Integral Eqns. Operator Theory | |
| dc.identifier | https://arxiv.org/abs/0704.1966 | |
| dc.identifier | http://arxiv.org/abs/0704.1966 | |
| dc.identifier | Integral Equations Operator Theory 59 (2007) no. 3, 329-343 | |
| dc.identifier | doi:10.1007/s00020-007-1534-9 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154694 | |
| dc.subject | Complex Variables | |
| dc.subject | Operator Algebras | |
| dc.subject | 30E05, 47A56 (Primary); 32F45 (Secondary) | |
| dc.title | Some new observations on interpolation in the spectral unit ball | |
| dc.type | text |