A Methodology for the Constructive Approximation of Nonlinear Operators Defined in Non Compact Sets
| dc.contributor.author | Torokhti, A. | |
| dc.contributor.author | Howlett, P.G. | |
| dc.date.issued | 1997 | |
| dc.description.abstract | We consider the constructive approximation of a non-linear operator that is known on a bounded but not necessarily compact set. Our main result can be regarded as an extension of the classical Stone-Weierstrass Theorem and also shows that the approximation is stable to small disturbances. This problem arises in the modelling of real dynamical systems where an input-output mapping is known only on some bounded subset of the input space. In such cases it is desirable to construct a model of the real system with a complete input-output map that preserves, in some approximate sense, the known mapping. The model is normally constructed from an algebra of elementary continuous functions. We will assume that the input space is a separable Hilbert space. To solve the problem we introduce a special weak topology and show that uniform continuity of the given operator in the weak topology provides an alternative compactness condition that is sufficient to justify the desired approximation. | |
| dc.identifier.citation | Numerical Functional Analysis and Optimization, 1997; 18(3-4):343-365 | |
| dc.identifier.doi | 10.1080/01630569708816764 | |
| dc.identifier.issn | 0163-0563 | |
| dc.identifier.issn | 1532-2467 | |
| dc.identifier.uri | https://hdl.handle.net/1959.8/42685 | |
| dc.language.iso | en | |
| dc.publisher | Marcel Dekker | |
| dc.rights | Copyright status unknown | |
| dc.source.uri | https://doi.org/10.1080/01630569708816764 | |
| dc.title | A Methodology for the Constructive Approximation of Nonlinear Operators Defined in Non Compact Sets | |
| dc.type | Journal article | |
| pubs.publication-status | Published | |
| ror.mmsid | 9915912690801831 |