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Support Theorems and an Injectivity Result for Integral Moments of a Symmetric m-Tensor Field

  • Anuj Abhishek
  • Rohit Kumar MishraEmail author
Article

Abstract

In this work, we show an injectivity result and support theorems for integral moments of a symmetric m-tensor field on a simple, real analytic, Riemannian manifold. Integral moments of symmetric m-tensor fields were first introduced by Sharafutdinov. First we generalize a Helgason type support theorem proven by Krishnan and Stefanov (Inverse Probl Imaging 3(3):453–464, 2009). We use this extended result along with the first integral moments of a symmetric m-tensor field to prove the aforementioned results.

Keywords

Integral moments Analytic microlocal analysis Support theorems 

Mathematics Subject Classification

47G10 47G30 53B21 

Notes

Acknowledgements

We would like to thank Prof. Vladimir Sharafutdinov for suggesting this problem. Besides, we would also like to express our sincere gratitude to Prof. Todd Quinto and Prof. Venky Krishnan for several hours of fruitful discussions. The authors benefited from the support of the Airbus Group Corporate Foundation Chair “Mathematics of Complex Systems” established at TIFR Centre for Applicable Mathematics and TIFR International Centre for Theoretical Sciences, Bangalore, India. Finally, we would like to thank the referee for their helpful comments and suggestions.

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Authors and Affiliations

  1. 1.Department of MathematicsTufts UniversityMedfordUSA
  2. 2.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

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