A Variation of Lp Uncertainty Principles in Weinstein Setting

Ahmed Saoudi ()
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Ahmed Saoudi: Northern Border University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1697-1712

Abstract: Abstract The Weinstein operator has several applications in pure and applied Mathematics especially in Fluid Mechanics and satisfies some uncertainty principles similar to the Euclidean Fourier transform. The aim of this paper is establish a generalization of uncertainty principles for Weinstein transform in L α p -norm. Firstly, we extend the Heisenberg-Pauli-Weyl uncertainty principle to more general case. Then we establish three continuous uncertainty principles of concentration type. The first and the second uncertainty principles are L α p versions and depend on the sets of concentration Ω and Σ, and on the time function ϕ. However, the third uncertainty principle is also L α p version depends on the sets of concentration and he is independent on the band limited function ϕ. These L α p -Donoho-Stark-type inequalities generalize the results obtained in the case p = q = 2.

Keywords: Weinstein operator; Heisenberg-Pauli-Weyl-type inequality; concentration uncertainty principles; Donoho-Stark-type inequality; 43A32; 44A15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0490-9

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