Fredholm Property of Fourier Integral Operators - Aid, Omar Farouk; Senoussaoui, Abderrahmane; Slimani, Mahmoud (Discontinuity, Nonlinearity, and Complexity, 2026)
In this work, we present the necessary notations and background information that will be used throughout our paper. We begin by introducing some foundational concepts regarding Fredholm operators, providing the essential context for our subsequent analysis. Next, we delve into fundamental principles from the theory of a specific class of Fourier integral operators, focusing on symbols and phase functions. These elements form the cornerstone of our primary objective. Furthermore, we prove significant results concerning the composition of Fourier integral operators with their $L^{2}$-adjoints. These findings are crucial as they enable us to derive important conclusions about the Fredholm properties of these operators.