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

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, wh...

Full description

Saved in:
Bibliographic Details
Published in:Analysis and mathematical physics 2023-08, Vol.13 (4), Article 56
Main Author: Rubin, Boris
Format: Article
Language:English
Subjects:
Analysis
Diameters
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Radon transformation
Tubes
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 ( R n ) 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 R 2 and a similar transform over tubes of fixed diameter in R 3 , are considered.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-023-00819-5