On the representation by linear superpositions |
| |
Authors: | Vugar E Ismailov |
| |
Institution: | aMathematics and Mechanics Institute, Azerbaijan National Academy of Sciences, Az-1141 Baku, Azerbaijan |
| |
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. |
| |
Keywords: | Linear superposition Closed path Ridge function |
本文献已被 ScienceDirect 等数据库收录! |
|