Compact weighted composition operators and fixed points in convex domains
| dc.creator | Clahane, Dana D. | |
| dc.date | 2005-12-02 | |
| dc.date | 2006-05-12 | |
| dc.date.accessioned | 2026-07-07T06:54:46Z | |
| dc.date.available | 2026-07-07T06:54:46Z | |
| dc.description | We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward the boundary of D, and p is a holomorphic self-map of D such that the weighted composition operator W assigning the product of m and the composition of f and p to a given function f is compact on a holomorphic functional Hilbert space (containing the polynomial functions densely) on D with reproducing kernel K blowing up along the diagonal of D toward its boundary, then p has a unique fixed point in D. We apply this result by making a reasonable conjecture about the spectrum of W based on previous one-variable and multivariable results concerning compact weighted and unweighted composition operators. | |
| dc.description | 10 pages. Corrected a few typographical errors and an error in one step of the main result's proof. This paper was presented in September 2005 at the Wabash Extramural Modern Analysis Mini-conference in Indianapolis | |
| dc.identifier | https://arxiv.org/abs/math/0512044 | |
| dc.identifier | http://arxiv.org/abs/math/0512044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106058 | |
| dc.subject | Functional Analysis | |
| dc.subject | Complex Variables | |
| dc.subject | 47B33; 32A10 | |
| dc.title | Compact weighted composition operators and fixed points in convex domains | |
| dc.type | text |