Asymptotic uncorrelation for Mexican needlets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:363

Article

Mayeli, Azita

关键词: Spherical harmonics;    Spherical Laplacian operator;    Wavelets;    Mexican needlets;    Second-order isotropy;    Angular power spectrum;    Legendre (Gegenbauer) polynomials;   

DOI  :  10.1016/j.jmaa.2009.07.044

来源: Elsevier

【 摘 要 】

We recall Mexican needlets from [D. Geller, A. Mayeli, Continuous wavelets on compact manifolds, Math. Z. 262 (4) (2009) 895-927; D. Geller, A. Mayeli, Nearly tight frames and space-frequency analysis on compact manifolds, Math. Z. 263 (2) (2009) 234-264]. We derive an estimate for certain types of Legendre series, which we apply to the statistical properties of Mexican needlets. More precisely, we shall show that, under isotropy assumption, the Mexican needlet coefficients of a random field on the sphere are asymptotically uncorrelated, as the frequency parameter goes to infinity. This property is important in the analysis of spherical random fields, in particular in connection to the analysis of Cosmic Microwave Background (CMB) radiation data. Published by Elsevier Inc.

【 授权许可】

Free