Biorthogonal multiresolution analysis on a triangle and applications

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:288

Article

Ajmi, Neyla¹  Jouini, Abdellatif¹  Rieusset, Pierre Gilles Lemarie² 

[1] Univ Tunis El Manor, Fac Sci Tunis, Lab Anal Math & Applicat LR11ES11, Tunis 2092, Tunisia

[2] Univ Evry, Lab Math & Modelisat Evry, UMR 8071, F-91037 Evry, France

关键词: Projection operator;    Scaling filter;    Riesz basis;    Scaling space;    Wavelet;    Sobolev space;   

DOI  :  10.1016/j.cam.2015.04.009

来源: Elsevier

【 摘 要 】

We present in this paper new constructions of biorthogonal multiresolution analysis on the triangle Delta. We use direct method based on the tensor product to construct dual scaling spaces on Delta. Next, we construct the associated wavelet spaces and we prove that the associated wavelets have compact support and preserve the original regularity. Finally, we describe some regular results which are very useful to establish the norm equivalences. As applications, we prove that the wavelet bases constructed in this paper are adapted for the study of the Sobolev spaces H-0(s)(Delta) and H-s(Delta) (s is an element of N) and are easy to implement. Published by Elsevier B.V.

【 授权许可】

Free