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 subspace
†This work was supported in part by contract number N 00014-67-A-0128-004 at the University of Wisconsin, from which the first author is one leave, and by grant USAFOSR 69-1812B at the Center for Numerical Analysis at the University of Texas
†This work was supported in part by contract number N 00014-67-A-0128-004 at the University of Wisconsin, from which the first author is one leave, and by grant USAFOSR 69-1812B at the Center for Numerical Analysis at the University of Texas
Notes
†This work was supported in part by contract number N 00014-67-A-0128-004 at the University of Wisconsin, from which the first author is one leave, and by grant USAFOSR 69-1812B at the Center for Numerical Analysis at the University of Texas