Transmutation via the momentum plane

Abstract

AbstractTransmutation methods are developed for equations of the form x2 φ“ + x2(k2” ‐ q̃(x)) φ = (v2 ‐ (1/4)) φ, with v as spectral variable, which correspond to problems in quantum scattering theory at fixed energy k2 (here v ˜ l + (1/2) with l complex angular momentum). Spectral formulas for transmutation kernels are constructed and the machinery of transmutation theory developed by the author for spectral variable k is shown to have a version here. General Kontrorovič‐Lebedev theorems are also proved.