Name
Abstract | ||
|---|---|---|
In a number of papers, Y. Sternfeld investigated the problems of representation of continuous and bounded functions by linear superpositions. In particular, he proved that if such representation holds for continuous functions, then it holds for bounded functions. We consider the same problem without involving any topology and establish a rather practical necessary and sufficient condition for representability of an arbitrary function by linear superpositions. In particular, we show that if some representation by linear superpositions holds for continuous functions, then it holds for all functions. This will lead us to the analogue of the well-known Kolmogorov superposition theorem for multivariate functions on the d-dimensional unit cube. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.jat.2007.09.003 | Journal of Approximation Theory |
Keywords | Field | DocType |
sufficient condition,arbitrary function,y. sternfeld,continuous function,d-dimensional unit cube,linear superpositions,bounded function,well-known kolmogorov superposition theorem,multivariate function,linear superposition | Superposition theorem,Continuous function,Superposition principle,Algebra,Mathematical analysis,Unit cube,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
151 | 2 | J. Approx. Theory 151 (2008), 113-125 |
Citations | PageRank | References |
1 | 0.63 | 1 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vugar E. Ismailov | 1 | 27 | 4.46 |