Hybrid spline frames

Abstract

Abstract. Using their unitary extension principle, Ron and Shen have constructed a normalized tight frame for L 2 (R) consisting of spline functions with uniform knots. This paper constructs a normalized tight frame for L 2 ((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 L 2 ((0, ∞)) based on dilation and translation.