STRUCTURE AND DIFFERENTIAL PROPERTIES OF 2D TENSOR FIELDS OF SMALL RANKS

The Radon transform generates many other integral transforms in integral geometry and tensor tomography. Together with complicated geometrical objects, the weighted ray and Radon transforms arise. Usually symmetric tensor fields are considered as the object should be reconstructed. We consider complete, symmetric and difference non-symmetric tensor fields of small ranks as the objects for applications in integral geometry and tensor tomography. The structure and differential properties of such fields are investigated. We establish a decomposition theorem for a complete tensor field, properties and attributes of solenoidal and potential fields.