On the theorem of M.Golomb
| dc.creator | Ismailov, Vugar | |
| dc.date | 2007-08-26 | |
| dc.date | 2008-07-10 | |
| dc.date.accessioned | 2026-07-07T09:49:13Z | |
| dc.date.available | 2026-07-07T09:49:13Z | |
| dc.description | Let $X_{1},...,X_{n}$ be compact spaces and $X=X_{1}\times ... \times X_{n}.$ Consider the approximation of a function $f\in C(X)$ by sums $g_{1}(x_{1})+... g_{n}(x_{n}),$ where $g_{i}\in C(X_{i}),$ $i=1,...,n.$ In [8], M.Golomb obtained a formula for the error of this approximation in terms of measures constructed on special points of $X$, called "projection cycles". However, his proof had a gap, which was pointed out by Marshall and O'Farrell [15]. But the question if the formula was correct, remained open. The purpose of the paper is to prove that Golomb's formula holds in a stronger form. | |
| dc.description | 8 pages; the previous main result has substantially improved | |
| dc.identifier | https://arxiv.org/abs/0708.3503 | |
| dc.identifier | http://arxiv.org/abs/0708.3503 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164505 | |
| dc.subject | Functional Analysis | |
| dc.subject | 41A30, 41A50, 41A63 | |
| dc.title | On the theorem of M.Golomb | |
| dc.type | text |