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PreprintCC BY 4.0arXiv

Resolvent bounds and eigenvalue estimates of generalized Schrödinger operators with complex potentials on compact manifolds

  • Eduard Stefanescu
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Abstract

We extend Cuenin's compact-manifold spectral bounds for Schrödinger operators with complex potentials to a general pseudodifferential setting. More precisely, we study operators P+V, where P is a positive self-adjoint elliptic classical pseudodifferential operator of positive order and V is complex-valued. The main analytic input is a resolvent principle showing that spectral cluster estimates for P imply Lp-Lp' resolvent estimates along suitable complex curves. Combined with Sogge's spectral cluster bounds, this yields exterior-region resolvent estimates extending those of Krupchyk and Uhlmann; we also prove direct resolvent bounds in the interior region. On Zoll manifolds, we discuss the sharpness of the resulting spectral bounds.

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Cite

BibTeXRIS
BibTeX
@misc{stefanescu2026resolvent,
  title = {{Resolvent bounds and eigenvalue estimates of generalized Schrödinger operators with complex potentials on compact manifolds}},
  author = {Eduard Stefanescu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10127},
  eprint = {2609.10127},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10127},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Resolvent bounds and eigenvalue estimates of generalized Schrödinger operators with complex potentials on compact manifolds
AU  - Eduard Stefanescu
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10127
UR  - https://arxiv.org/abs/2609.10127
AB  - We extend Cuenin's compact-manifold spectral bounds for Schrödinger operators with complex potentials to a general pseudodifferential setting. More precisely, we study operators P+V, where P is a positive self-adjoint elliptic classical pseudodifferential operator of positive order and V is complex-valued. The main analytic input is a resolvent principle showing that spectral cluster estimates for P imply L^p-L^p' resolvent estimates along suitable complex curves. Combined with Sogge's spectral cluster bounds, this yields exterior-region resolvent estimates extending those of Krupchyk and Uhlmann; we also prove direct resolvent bounds in the interior region. On Zoll manifolds, we discuss the sharpness of the resulting spectral bounds.
ER  -