Nonstationary subdivision schemes and multiresolution analysis

Albert Cohen, Nira Dyn

Research output: Contribution to journalArticlepeer-review

Abstract

Nonstationary subdivision schemes consist of recursive refinements of an initial sparse sequence with the use of masks that may vary from one scale to the next finer one. This paper is concerned with both the convergence of nonstationary subdivision schemes and the properties of their limit functions. We first establish a general result on the convergence of such schemes to C compactly supported functions. We show that these limit functions allow us to define a multiresolution analysis that has the property of spectral approximation. Finally, we use these general results to construct C compactly supported cardinal interpolants and also C compactly supported orthonormal wavelet bases that constitute Riesz bases for Sobolev spaces of any order.

Original languageEnglish
Pages (from-to)1745-1769
Number of pages25
JournalSIAM Journal on Mathematical Analysis
Volume27
Issue number6
DOIs
StatePublished - Nov 1996

Keywords

  • Dyadic interpolation
  • Multiresolution analysis
  • Spectral approximation
  • Subdivision schemes
  • Wavelets

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