Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Autor:	Jagdish N. Pandey
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	wavelet transform continuous wavelet transform window functions integral transform of generalized functions Schwartz distributions Mathematics QA1-939
Zdroj:	Symmetry, Vol 13, Iss 7, p 1106 (2021)
Druh dokumentu:	article
ISSN:	13071106 2073-8994
DOI:	10.3390/sym13071106
Popis:	We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/e0e3436fd65541d99d029a843a6d6406 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
Nepřihlášeným uživatelům se plný text nezobrazuje	K zobrazení výsledku je třeba se přihlásit.