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E-ISSN: 2788-9327

P-ISSN: 1606-8947

Vol. 24 No. 2 (2020)

Phase space localization of orthonormal sequences in \(L_α^2 (R_+^d)\)

  • Amgad Rashed Naji Faculty of Education - Yafa'a, University of Aden
  • Ammer Zain Othman Faculty of Education - Yafa'a, University of Aden

University of Aden Journal of Natural and Applied Sciences, Vol. 24 No. 2 (2020), 31-10-2020 Page 463-474

DOI:

https://doi.org/10.47372/uajnas.2020.n2.a13

Abstract

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
$${^{sup}_n (‖{|x-e_n | ɸ_n }‖_{L_α^2 (R_+^d ) } ‖{|ξ-a_n | F_W (ɸ_n )}‖_{L_α^2 (R_+^d ) } )<∞}$$

Keywords:
    Weinstein operator, Uncertainty principle, Orthonormal bases, Time–frequency concentration

How to Cite

Naji, A. R., & Othman, A. Z. (2020). Phase space localization of orthonormal sequences in \(L_α^2 (R_+^d)\). University of Aden Journal of Natural and Applied Sciences, 24(2), 463–474. https://doi.org/10.47372/uajnas.2020.n2.a13
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