arXiv subjects

Frederick Opoku

Publications and source records attributed to Frederick Opoku.

2 recordsLinked to original sources

arXiv2026

Hyperbolic partial differential equations with complex characteristics on Fourier Lebesgue spaces

The aim of this paper is to establish well-posedness properties for hyperbolic PDEs on Fourier Lebesgue spaces. We consider hyperbolic operators with complex characteristics. Since our approach comes from harmonic analysis, we establish boundedness properties of Fourier integral operators with complex-valued phase functions on Fourier Lebesgue spaces, Besov spaces and Triebel-Lizorkin spaces. Indeed, these classes of operators serve as propagators of the considered PDE problems. In terms of the boundedness properties, we prove new results in the case where the canonical relation of the operator is assumed to satisfy the {\it spatial smooth factorization condition}

math.AP↗

arXiv2025

Boundedness of Fourier Integral Operators with complex phases on Fourier Lebesgue spaces

In this paper, we develop boundedness estimates for Fourier integral operators on Fourier Lebesgue spaces when the associated canonical relation is parametrised by a complex phase function. Our result constitutes the complex analogue of those obtained for real canonical relations by Rodino, Nicola, and Cordero. We prove that, under the spatial factorization condition of rank $\varkappa$, the corresponding Fourier integral operator is bounded on the Fourier Lebesgue space $\mathcal{F}L^p,$ provided that the order $m$ of the operator satisfies that $ m \leq -\varkappa\left|\frac{1}{p}-\frac{1}{2}\right|, 1 \leq p \leq \infty. $ This condition on the order $m$ is sharp.

math.AP↗