Open AccessPhase space localization of orthonormal sequences in \(L_α^2 (R_+^d)\)
Author(s) -
Amgad Rashed Naji,
Ammer Zain Othman
Publication year - 2020
Publication title -
mağallaẗ ğāmi'aẗ 'adan li-l-'ulūm al-ṭabīyyaẗ wa-al-taṭbīqiyyaẗ
Language(s) - English
Resource type - Journals
eISSN - 2788-9327
pISSN - 1606-8947
DOI - 10.47372/uajnas.2020.n2.a13
Subject(s) - orthonormal basis , combinatorics , bounded function , mathematics , space (punctuation) , operator (biology) , physics , mathematical analysis , philosophy , chemistry , linguistics , repressor , quantum mechanics , transcription factor , gene , biochemistry
In this article, we prove Malinnikova’s result for Weinstein operator as follows: Let \({(ɸ_n)}_{n=1}^∞\) be an orthonormal basis for \(L_α^2 (R_+^d )\). If the sequences \({(e_n)}_{n=1}^∞⊂R_+^d\) and \({(a_n)}_{n=1}^∞⊂R_+^d\) are bounded, then$${^{sup}_n (‖{|x-e_n | ɸ_n }‖_{L_α^2 (R_+^d ) } ‖{|ξ-a_n | F_W (ɸ_n )}‖_{L_α^2 (R_+^d ) } )<∞}$$