On the closedness of the linear image of a set with applications to generalized spline functions †
- 1 January 1974
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 4 (3) , 191-205
- https://doi.org/10.1080/00036817408839091
Abstract
In many problems of approximation theory, especially in the field of spline functions and their generalizations, one seeks a u minimizing ||Tu-f|| for u in some constraint set U; it is usually easy to prove existence of such a u if IT/is closed. We consider hypotheses that will guarantee the closedness of TU, and, more generally, the closedness of the sum of U and a closed linear subspaceKeywords
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