A class of orthogonal refinable functions and wavelets

TY - JOUR

T1 - A class of orthogonal refinable functions and wavelets

AU - Goodman, Timothy

N1 - dc.publisher: Springer

PY - 2003

Y1 - 2003

N2 - We give a construction, for any n 2, of a space S of spline functions of degree n – 1 with simple knots in (1/4)Z which is generated by a triple of refinable, orthogonal functions with compact support. Indeed, the result holds more generally by replacing the B-spline of degree n – 1 with simple knots at the integers by any continuous refinable function whose mask is a Hurwitz polynomial of degree n. A simple construction is also given for the corresponding wavelets.

AB - We give a construction, for any n 2, of a space S of spline functions of degree n – 1 with simple knots in (1/4)Z which is generated by a triple of refinable, orthogonal functions with compact support. Indeed, the result holds more generally by replacing the B-spline of degree n – 1 with simple knots at the integers by any continuous refinable function whose mask is a Hurwitz polynomial of degree n. A simple construction is also given for the corresponding wavelets.

KW - Wavelet

KW - Multiwavelet

KW - B-spline

KW - Orthogonal

U2 - 10.1007/s00365-003-0535-4

DO - 10.1007/s00365-003-0535-4

M3 - Article

SN - 0176-4276

VL - 19

SP - 525

EP - 540

JO - Constructive Approximation

JF - Constructive Approximation

IS - 4

ER -