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PreprintarXiv licencearXiv

Local Smoothing Estimates of Schrödinger Operators on Waveguides Using Refined Decoupling

  • Wenchang Sun
  • Jiheng Tan
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Abstract

We establish improved local smoothing estimates for the Schrödinger equation on waveguides. Our results extend the previously known range of exponents in every dimension and are sharp in certain cases. The proof develops a transference argument that preserves the discrete periodic frequency structure, together with a refined decoupling estimate adapted to waveguides. We also derive consequences for Euclidean local smoothing and almost everywhere convergence.

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Cite

BibTeXRIS
BibTeX
@misc{sun2026local,
  title = {{Local Smoothing Estimates of Schrödinger Operators on Waveguides Using Refined Decoupling}},
  author = {Wenchang Sun and Jiheng Tan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41219},
  eprint = {2610.41219},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41219},
}
RIS
TY  - UNPB
TI  - Local Smoothing Estimates of Schrödinger Operators on Waveguides Using Refined Decoupling
AU  - Wenchang Sun
AU  - Jiheng Tan
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41219
UR  - https://arxiv.org/abs/2610.41219
AB  - We establish improved local smoothing estimates for the Schrödinger equation on waveguides. Our results extend the previously known range of exponents in every dimension and are sharp in certain cases. The proof develops a transference argument that preserves the discrete periodic frequency structure, together with a refined decoupling estimate adapted to waveguides. We also derive consequences for Euclidean local smoothing and almost everywhere convergence.
ER  -