On the injectivity of integral operators related to the Euler–Poisson–Darboux equation and shifted k-plane transforms

Authors

Boris Rubin, Louisiana State University

Document Type

Article

Publication Date

8-1-2023

Abstract

We study injectivity of integral operators which map the Cauchy initial data for the Euler–Poisson–Darboux equation to the fixed time measurement of the solution of this equation. These operators generalize the well-known spherical means and are closely related to the shifted k-plane transforms, which assign to functions in L^p(Rⁿ) their mean values over all k-planes at a fixed distance from the given k-planes. Several generalizations, including the Radon transform over strips of fixed width in R² and a similar transform over tubes of fixed diameter in R³ , are considered.

Publication Source (Journal or Book title)

Analysis and Mathematical Physics

Recommended Citation

Rubin, B. (2023). On the injectivity of integral operators related to the Euler–Poisson–Darboux equation and shifted k-plane transforms. Analysis and Mathematical Physics, 13 (4) https://doi.org/10.1007/s13324-023-00819-5