Commuting integral and differential operators and the master symmetries of the Korteweg–de Vries equation. (27th July 2021)

• Record Type: Journal Article
• Authors: Grünbaum, F Alberto
• Is Part Of: Inverse problems. Volume 37:Number 8(2021)
• Publication Date: 2021-07-27
• Subjects: commuting -- integral -- differential -- operators -- master -- symmetries; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac11c6
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The singular value decomposition going with many problems in medical imaging, non-destructive testing, geophysics, etc is of central importance. Unfortunately the effective numerical determination of the singular functions in question, is a very ill-posed problem. The best known remedy to this problem goes back to the work of Slepian et al (1960–1965 Bell Labs). We show that the master symmetries of the Korteweg–de Vries equation give a way to extend the remarkable result of Slepian in connection with the Bessel integral kernel and the existence of a differential operator that commutes with the corresponding integral operator. The original results of Bell Labs group has already played an important role in the study of the limited angle problem in x-ray tomography as well as in random matrix theory.