RIESZ BASES OF SPLINES AND REGULARIZED SPLINES WITH MULTIPLE KNOTS

This paper deals with L(2)(R)-norm and Sobolev-norm stability or polyn omial splines with multiple knots, and with regularized versions there of. An essential ingredient is a result on Holder continuity of the sh ift operator operating on a B-spline series. The stability estimates c an be reformulated in terms of a Riesz basis property for the underlyi ng spline spaces. These can also be employed to derive a result on sta ble Hermite interpolation on the real line. We point to the connection with the problem of symmetric preconditioning of bi-infinite interpol ation matrices. (C) 1996 Academic Press, Inc.