## Strichartz estimates for the Schrödinger equation with a measure-valued potential

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M. Burak Erdoğan, Michael Goldberg and William R. Green
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**8**(2021), 336-348

## Abstract:

We prove Strichartz estimates for the Schrödinger equation in $\mathbb {R}^n$, $n\geq 3$, with a Hamiltonian $H = -\Delta + \mu$. The perturbation $\mu$ is a compactly supported measure in $\mathbb {R}^n$ with dimension $\alpha > n-(1+\frac {1}{n-1})$. The main intermediate step is a local decay estimate in $L^2(\mu )$ for both the free and perturbed Schrödinger evolution.## References

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## Additional Information

**M. Burak Erdoğan**- Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
- MR Author ID: 629150
- Email: berdogan@illinois.edu
**Michael Goldberg**- Affiliation: Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221
- MR Author ID: 674280
- ORCID: 0000-0003-1039-6865
- Email: goldbeml@ucmail.uc.edu
**William R. Green**- Affiliation: Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803
- MR Author ID: 906481
- ORCID: 0000-0001-9399-8380
- Email: green@rose-hulman.edu
- Received by editor(s): August 7, 2019
- Published electronically: November 22, 2021
- Additional Notes: The first author was partially supported by NSF grant DMS-1501041.

The second author was supported by Simons Foundation Grant 281057.

The third author was supported by Simons Foundation Grant 511825. - Communicated by: Alexander Iosevich
- © Copyright 2021 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B
**8**(2021), 336-348 - MSC (2020): Primary 35Q40; Secondary 42B15
- DOI: https://doi.org/10.1090/bproc/79
- MathSciNet review: 4343929