Finite-part Integration of the Hilbert Transform

• Main Authors: Blancas, Philip Jordan D., Galapon, Eric A.
• Format: text
• Published: Archīum Ateneo 2025
• Subjects: divergent integrals; finite-part integrals; Hilbert transform; Mellin transform; Atomic, Molecular and Optical Physics; Physical Sciences and Mathematics; Physics
• Online Access: https://archium.ateneo.edu/roses-lab/1; https://doi.org/10.1080/10652469.2025.2454955
• Institution: Ateneo De Manila University

The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [Galapon EA. The problem of missing terms in term-by-term integration involving divergent integrals. Proc R Soc A. 2017;473:20160567]. In general, the result consists of two terms–the fi...