Hybrid spline frames

Abstract

Using their unitary extension principle, Ron and Shen have constructed a normalized tight frame for L2(R{double-struck}) consisting of spline functions with uniform knots. This paper constructs a normalized tight frame for L2((0,∞)) comprising spline functions with knots on a hybrid of uniform and geometric mesh. The construction is motivated by applications in adaptive approximation using spline functions on a hybrid mesh that admits a natural dyadic multiresolution approximation of L2((0,∞)) based on dilation and translation. © 2009 American Mathematical Society.