Abstract
We study unique continuation inequalities for the free Schrödinger equation in the context of Riemannian symmetric spaces of noncompact type. The results imply that if the solution is small at two different times outside sets of finite measure, then the solution is small in the whole space. On the Euclidean spaces, these inequalities are equivalent to certain uncertainty principles in harmonic analysis.
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Acknowledgements
The authors are greatly indebted to the referee for the careful reading of the manuscript and for many useful suggestions.
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Funding was provided by Department of Science and Technology, India (Grant No. IFA19-MA136).
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The Mithun Bhowmik is supported by the Department of Science and Technology, India (INSPIRE Faculty Award IFA19-MA136).
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Bhowmik, M., Ray, S.K. Unique continuation inequalities for Schrödinger equation on Riemannian symmetric spaces of noncompact type. Annali di Matematica 203, 331–343 (2024). https://doi.org/10.1007/s10231-023-01365-4
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DOI: https://doi.org/10.1007/s10231-023-01365-4
Keywords
- Riemannian symmetric space
- Unique continuation
- Uncertainty Principles
- Schrödinger equation
- Benedicks’ theorem