A new approach to interpolating scaling functions

Abstract

We present a new method to construct interpolating refinable functions in higher dimensions. The approach is based on the solutions to specific Lagrange interpolation problems by polynomials and applies to a large class of scaling matrices. The resulting scaling functions automatically satisfy certain Strang-Fix conditions. Several examples are discussed.

Keywords:

• Interpolating scaling functions
• strang-fix conditions
• polynomial interpolation
• expanding scaling matrices

AMS:

• 41A05
• 41A30
• 41A63

^*The work of this author has been supported by Deutsche Forschungsgemeinschaft (DA 117113-1)

^*The work of this author has been supported by Deutsche Forschungsgemeinschaft (DA 117113-1)

Notes

^*The work of this author has been supported by Deutsche Forschungsgemeinschaft (DA 117113-1)