2013/05/15 by Pierre Schapira · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic analysis #Algebraic number #Cauchy distribution #Cauchy problem #Differential (mechanical device) #Differential algebraic equation #Differential equation #Fourier integral operator #Hyperbolic function #Hyperbolic manifold #Hyperbolic partial differential equation #Initial value problem #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematical proof #Mathematics #Microlocal analysis #Nonlinear Waves and Solitons #Operator theory #Ordinary differential equation #Partial derivative #Partial differential equation #Physics #Pure mathematics #advanced mathematical theories #math-ph #math.AG #math.AP #math.MP #msc:35A27 #msc:58J15 #msc:58J45 #msc:81T20
paper · pdf · doi:10.1007/s11005-013-0637-2
To appear in Letters in Mathematical Physics
arxiv created 2013/05/15 · openalex publication_date 2013/06/15 · arxiv updated 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This is essentially a survey paper in which we solve the global Cauchy problem on causal manifolds for hyperbolic systems of linear partial differential equations in the framework of hyperfunctions. Besides the classical Cauchy-Kowalevsky theorem, our proofs only use tools from the microlocal theory of sheaves, that is, tools of purely algebraic and geometric nature.