Biorthogonal multiresolution analysis on a triangle and applications

作者：

Highlights：

• Wavelets have unfolded their full computation efficiently in numerical and applied analysis.

• The properties of wavelet bases provide a rigorous analysis for dynamical systems.

• We construct in this work biorthogonal wavelet bases on a triangle.

• These bases are adapted to the study of the Sobolev spaces.

• The bases allow many concrete numerical examples as numerical simulation for elliptic problems or image processing.

摘要

•Wavelets have unfolded their full computation efficiently in numerical and applied analysis.•The properties of wavelet bases provide a rigorous analysis for dynamical systems.•We construct in this work biorthogonal wavelet bases on a triangle.•These bases are adapted to the study of the Sobolev spaces.•The bases allow many concrete numerical examples as numerical simulation for elliptic problems or image processing.

论文关键词：Projection operator,Scaling filter,Riesz basis,Scaling space,Wavelet,Sobolev space

论文评审过程：Received 12 July 2013, Revised 6 January 2015, Available online 23 April 2015, Version of Record 15 May 2015.

论文官网地址：https://doi.org/10.1016/j.cam.2015.04.009