2017/08/31 by Felix Finster, Margarita Kraus
Mathematics · Physics and Astronomy · #Applied mathematics #Backus–Gilbert method #Black Holes and Theoretical Physics #Cauchy distribution #Cosmology and Gravitation Theories #Geodesic #Hadamard transform #Inverse problem #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Pure mathematics #Regularization (linguistics) #Regularization perspectives on support vector machines #Tikhonov regularization #gr-qc #math-ph #math.AP #math.MP
paper · pdf · doi:10.1016/j.jmaa.2020.124340
published as J. Math. Anal. Appl. 491 (2020) 124340 · 27 pages, LaTeX, 3 figures, minor changes (published version)
openalex publication_date 2020/07/01 · arxiv created 2020/07/06 · arxiv updated 2020/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A local expansion is proposed for two-point distributions involving an ultraviolet regularization in a four-dimensional globally hyperbolic space-time. The regularization is described by an infinite number of functions which can be computed iteratively by solving transport equations along null geodesics. We show that the Cauchy evolution preserves the regularized Hadamard structure. The resulting regularized Hadamard expansion gives detailed and explicit information on the global dynamics of the regularization effects.