Riesz bases of splines and regularized splines with multiple knots

[摘要] This paper deals with L(2)(R)-norm and Sobolev-norm stability or polynomial splines with multiple knots, and with regularized versions thereof. An essential ingredient is a result on Holder continuity of the shift operator operating on a B-spline series. The stability estimates can be reformulated in terms of a Riesz basis property for the underlying spline spaces. These can also be employed to derive a result on stable Hermite interpolation on the real line. We point to the connection with the problem of symmetric preconditioning of bi-infinite interpolation matrices. (C) 1996 Academic Press, Inc.

[发布日期] 1996-12-01