Generalized Radon Transforms On The Line And The Plane

This thesis is to study the generalized Radon transforms on the real line and on the plane. The Radon transform is an important subject in geometric analysis. In recent decades, the theory of Radon transforms developed very rapidly. It is used in study of many problems and is generalized in various situations with much progress. The theory of Radon transforms has an important position in applications as well, and it is one of the mathematical tools in the fields of Computed Tomography and reconstruction.The classical Radon transform is associated with the Lebesgue measure, the conclusions about it depend on the rotation-invariance and the translation-invariance of the Lebesgue measure, and the associated tools to it are the Laplacian and the Fourier transform. This paper is to study the generalized Radon transforms on the real line R~1 and...