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Analysis on Noncompact Manifolds and Index Theory: Fredholm Conditions and Pseudodifferential Operators

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Extended Abstracts 2021/2022 (GMC 2021)

Part of the book series: Trends in Mathematics ((RPGAPC,volume 3))

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Abstract

We provide Fredholm conditions for compatible differential operators on certain Lie manifolds (that is, on certain possibly non-compact manifolds with nice ends). We discuss in more detail the case of manifolds with cylindrical, hyperbolic, and Euclidean ends, which are all covered by particular instances of our results. We also discuss applications to Schrödinger operators with singularities of the form \(r^{-2\gamma }\), \(\gamma \in \mathbb R_+\).

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Acknowledgements

Support: authors Ivan Beschastnyi and Catarina Carvalho by FCT–Fundação para a Ciência e Tecnologia, projects UIDB/04106/2020 and UIDB/04721/2020, respectively. Author Victor Nistor by ANR grant OpART and Yu Qiao by NSFC (11971282).

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Authors and Affiliations

  1. CIDMA, University of Aveiro, Aveiro, Portugal

    Ivan Beschastnyi

  2. CEAFEL, Department of Matemática, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    Catarina Carvalho

  3. Université de Lorraine, CNRS, IECL, Metz, France

    Victor Nistor

  4. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, China

    Yu Qiao

Authors
  1. Ivan Beschastnyi
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  2. Catarina Carvalho
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  3. Victor Nistor
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  4. Yu Qiao
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Corresponding author

Correspondence to Victor Nistor .

Editor information

Editors and Affiliations

  1. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    Duván Cardona

  2. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    Joel Restrepo

  3. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    Michael Ruzhansky

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Beschastnyi, I., Carvalho, C., Nistor, V., Qiao, Y. (2024). Analysis on Noncompact Manifolds and Index Theory: Fredholm Conditions and Pseudodifferential Operators. In: Cardona, D., Restrepo, J., Ruzhansky, M. (eds) Extended Abstracts 2021/2022. GMC 2021. Trends in Mathematics(), vol 3. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-48579-4_1

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