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  1. Journal of Fourier Analysis and Applications
  2. Journal of Fourier Analysis and Applications : Volume 20
  3. Journal of Fourier Analysis and Applications : Volume 20, Issue 5, October 2014
  4. The Broken Ray Transform on the Square
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Journal of Fourier Analysis and Applications : Volume 23
Journal of Fourier Analysis and Applications : Volume 22
Journal of Fourier Analysis and Applications : Volume 21
Journal of Fourier Analysis and Applications : Volume 20
Journal of Fourier Analysis and Applications : Volume 20, Issue 6, December 2014
Journal of Fourier Analysis and Applications : Volume 20, Issue 5, October 2014
Sharp $$L^{p,\infty }\rightarrow L^q$$ Estimates for the Dyadic-Like Maximal Operators
On Fourier Re-Expansions
Fourier Duality in Integral Geometry and Reconstruction from Ray Integrals
A Family of Functions with Two Different Spectra of Singularities
A Consistent and Stable Approach to Generalized Sampling
Ulyanov-type Inequalities Between Lorentz–Zygmund Spaces
The Broken Ray Transform on the Square
Square Function Characterization of Weak Hardy Spaces
Optimal Frame Completions with Prescribed Norms for Majorization
A Note on Recent Papers by Grafakos and Teschl, and Estrada
Journal of Fourier Analysis and Applications : Volume 20, Issue 4, August 2014
Journal of Fourier Analysis and Applications : Volume 20, Issue 3, June 2014
Journal of Fourier Analysis and Applications : Volume 20, Issue 2, April 2014
Journal of Fourier Analysis and Applications : Volume 20, Issue 1, February 2014
Journal of Fourier Analysis and Applications : Volume 19
Journal of Fourier Analysis and Applications : Volume 18
Journal of Fourier Analysis and Applications : Volume 17
Journal of Fourier Analysis and Applications : Volume 16
Journal of Fourier Analysis and Applications : Volume 15
Journal of Fourier Analysis and Applications : Volume 14
Journal of Fourier Analysis and Applications : Volume 13
Journal of Fourier Analysis and Applications : Volume 12
Journal of Fourier Analysis and Applications : Volume 11
Journal of Fourier Analysis and Applications : Volume 10
Journal of Fourier Analysis and Applications : Volume 9
Journal of Fourier Analysis and Applications : Volume 8
Journal of Fourier Analysis and Applications : Volume 7
Journal of Fourier Analysis and Applications : Volume 6
Journal of Fourier Analysis and Applications : Volume 5
Journal of Fourier Analysis and Applications : Volume 4
Journal of Fourier Analysis and Applications : Volume 3

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The Broken Ray Transform on the Square

Content Provider SpringerLink
Author Hubenthal, Mark
Copyright Year 2014
Abstract We study a particular broken ray transform on the Euclidean unit square and establish injectivity and stability for $$C_{0}^{2}$$ perturbations of a vanishing absorption parameter $$\sigma \equiv 0$$ . Given an open subset $$E$$ of the boundary, we measure the attenuation of all broken rays starting and ending at $$E$$ with the standard optical reflection rule applied to $$\partial \Omega {\setminus } E$$ . Using the analytic microlocal approach of Frigyik et al. for the X-ray transform on generic families of curves, we show injectivity via a path unfolding argument under suitable conditions on the available broken rays. Then we show that with a suitable decomposition of the measurement operator via smooth cutoff functions, the associated normal operator is a classical pseudo differential operator of order $$-1$$ , which leads to the desired result.
Ending Page 1082
Page Count 33
Starting Page 1050
File Format PDF
ISSN 10695869
e-ISSN 15315851
Journal Journal of Fourier Analysis and Applications
Issue Number 5
Volume Number 20
Language English
Publisher Springer US
Publisher Date 2014-07-11
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Integral geometry Abstract Harmonic Analysis Mathematical Methods in Physics Inverse problems Pseudodifferential operators Fourier Analysis Signal, Image and Speech Processing Microlocal analysis Approximations and Expansions Partial Differential Equations Integral geometry; differential forms, currents, etc.
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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