On some integral operators appearing in scattering theory, and their resolutions

2019/09/04 by Richard, S., Umeda, T.
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1909.01712

Abstract

We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of scattering theory, but are independent of any perturbation theory. The Hilbert transform, the Hankel transform, and the finite interval Hilbert transform are among the operators considered.

Related

• Scattering theory and Banach space valued singular integrals
• Scattering matrix and functions of self-adjoint operators
• Scattering matrices and Dirichlet-to-Neumann maps
• Spectral theory of discontinuous functions of self-adjoint operators: essential spectrum
• Scattering matrices and Dirichlet-to-Neumann maps