Momentum ray transforms, II: range characterization in the Schwartz space
Venkateswaran P. Krishnan, Ramesh Manna, Suman Kumar Sahoo, V. A. Sharafutdinov
Abstract
Abstract The momentum ray transform I k integrates a rank m symmetric tensor field f over lines of with the weight t k : We give the range characterization for the operator on the Schwartz space of rank m smooth fast decaying tensor fields. In dimensions , the range is characterized by certain differential equations of order which generalize the classical John equations. In the two-dimensional case, the range is characterized by certain integral conditions which generalize the classical Gelfand–Helgason–Ludwig conditions.
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MathematicsCharacterization (materials science)Rank (graph theory)Space (punctuation)Tensor (intrinsic definition)Mathematical physicsDifferential operatorTensor fieldField (mathematics)Mathematical analysisRange (aeronautics)Order (exchange)Operator (biology)CombinatoricsPure mathematicsPhysicsExact solutions in general relativityBiochemistryGeneChemistryOpticsRepressorEconomicsTranscription factorFinanceComposite materialMaterials scienceLinguisticsPhilosophyNumerical methods in inverse problemsElectromagnetic Scattering and AnalysisAdvanced Mathematical Physics Problems