An uncertainty principle for the windowed Bochner-Fourier transform with the complex-valued window function

• Autorzy: Yaremenko Mykola

Identyfikatory

DOI

10.1515/jaa-2023-0120

• Języki publikacji: EN

Abstrakty

EN

The generalization of Hardy uncertainty principle for the windowed Bochner-Fourier transform on the Heisenberg group is proved. We consider a Bochner measurable function Ψ : G → X, where X is a completely separable Hilbert space X and Let G be a completely separable, unimodular, connected nilpotent Lie group. We establish that if ϕ ∈ CC(G) is a non-trivial window function and Ψ ∈ L2(G) satisfies ‖Vϕ(Ψ)(g, χ)‖HB ≤ c2(g) exp(−β‖χ‖2), β > 0, then Ψ = 0 almost everywhere.

Słowa kluczowe

EN

windowed Fourier transform; uncertainty principle; Heisenberg inequality; locally compact group; Bochner integral; Bochner space; Hardy group

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2024
• Tom: Vol. 30, nr 2
• Strony: 215--222
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Yaremenko Mykola

• Department of Partial Differential Equations, The National Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

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