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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Fredholm Property of Fourier Integral Operators

Discontinuity, Nonlinearity, and Complexity 14(4) (2025) 623--633 | DOI:10.5890/DNC.2025.12.001

Omar Farouk Aid, Abderrahmane Senoussaoui, Mahmoud Slimani

Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Ben Bella. B.P. 1524 El M'naouar, Oran, Algeria

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Abstract

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.

Acknowledgments

\bibitem{CES1} Agarwal, P., Ahsand, S., Akbare, M., Nawaz, R., and Cesarano, C. (2022), A reliable algorithm for solution of higher dimensional nonlinear $(1 + 1)$ and $(2 + 1)$ dimensional Volterra-Fredholm integral equations, \textit{Dolomites Research Notes on Approximation}, \textbf{14}, 18-25.

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