Wavelet expansions and asymptotic behavior of distributions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:370

Article

Saneva, Katerina²  Vindas, Jasson¹ 

[1] Univ Ghent, Dept Pure Math & Comp Algebra, B-9000 Ghent, Belgium

[2] Univ Ss Cyril & Methodius, Fac Elect Engn & Informat Technol, Skopje 1000, North Macedonia

关键词: Orthogonal wavelets;    Wavelet coefficients;    Abelian theorems;    Tauberian theorems;    Distributions;    Quasiasymptotics;    Slowly varying functions;    Asymptotic behavior of generalized;    functions;   

DOI  :  10.1016/j.jmaa.2010.04.041

来源: Elsevier

【 摘 要 】

We develop a distribution wavelet expansion theory for the space of highly time-frequency localized test functions over the real line S-0(R) subset of S(R) and its dual space S-0'(R), namely, the quotient of the space of tempered distributions modulo polynomials. We prove that the wavelet expansions of tempered distributions converge in S-0'(R). A characterization of boundedness and convergence in S-0'(R) is obtained in terms of wavelet coefficients. Our results are then applied to study local and non-local asymptotic properties of Schwartz distributions via wavelet expansions. We provide Abelian and Tauberian type results relating the asymptotic behavior of tempered distributions with the asymptotics of wavelet coefficients. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free