Tomography such as X-ray transform or Radon transform is a very effective tool in a variety of areas and Harmonic analysis is not an exception.
In 2020 Bennett and Nakamura revealed an interesting connection between Radon transform and extension operator on the sphere, a typical (n-1)-dimensional submanifold.
In this talk, I will explain our recent results that generalize their results in any intermediate dimensional manifolds. Consequently, our identity gives a new perspective of the identity obtained by Bennett--Iliopoulou as an application. This work is based on joint work with Jon Bennett and Shohei Nakamura.