2007/06/27 by Khosrow Chadan, Chadan, Khosrow
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0706.3986
arxiv created 2007/06/27 · openalex publication_date 2007/06/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the integral representations of the solutions of Schrödinger equation, which are the essential ingredients of the Gel'fand-Levitan and Marchenko integral equations of inverse scattering theory, we obtain a general theorem on the positivity of some integral transforms, and extend the theorem of Bochner on Fourier transforms of functions of positive type to more general transforms. The present study is restricted to the positive half-axis. We then obtain a theorem on the positivity of Fourier cosine transform of the phase-shifts.