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Schrödinger operators with accretive potentials in weighted spaces

  • Borbala Gerhat
  • Petr Siegl
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Abstract

We analyse Schrödinger operators with accretive potentials in weighted spaces. We find conditions on potentials and weights for which the Dirichlet realisation, introduced by generalised form methods, has non-empty resolvent set. We establish a domain and graph norm separation property, as well as sufficient conditions for the compactness and Schatten class of the resolvent. Moreover, we investigate the relation between discrete spectra and eigenfunctions of operators in standard and weighted spaces. As applications we extend results on the completeness of eigensystems of operators with accretive potentials from standard to weighted spaces and analyse operator matrices exhibiting a Schur dominance property, in particular, related to a wave equation with strong accretive damping.

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Cite

BibTeXRIS
BibTeX
@misc{gerhat2026schrödinger,
  title = {{Schrödinger operators with accretive potentials in weighted spaces}},
  author = {Borbala Gerhat and Petr Siegl},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25826},
  eprint = {2609.25826},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25826},
}
RIS
TY  - UNPB
TI  - Schrödinger operators with accretive potentials in weighted spaces
AU  - Borbala Gerhat
AU  - Petr Siegl
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25826
UR  - https://arxiv.org/abs/2609.25826
AB  - We analyse Schrödinger operators with accretive potentials in weighted spaces. We find conditions on potentials and weights for which the Dirichlet realisation, introduced by generalised form methods, has non-empty resolvent set. We establish a domain and graph norm separation property, as well as sufficient conditions for the compactness and Schatten class of the resolvent. Moreover, we investigate the relation between discrete spectra and eigenfunctions of operators in standard and weighted spaces. As applications we extend results on the completeness of eigensystems of operators with accretive potentials from standard to weighted spaces and analyse operator matrices exhibiting a Schur dominance property, in particular, related to a wave equation with strong accretive damping.
ER  -