Index theorems for Fredholm, semi-Fredholm, and almost periodic operators: all in one example

DOI10.4171/JNCG/349zbMath1440.81039arXiv1711.07113MaRDI QIDQ2180245

Serge Richard, Hideki Inoue

Publication date: 13 May 2020

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.07113

zbMATH Keywords

Fredholm operatorscattering theoryindex theoremalmost periodicsemi-Fredholm operator

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (Semi-) Fredholm operators; index theories (47A53) Index theory and related fixed-point theorems on manifolds (58J20) Noncommutative geometry in quantum theory (81R60) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Related Items (3)

η-INVARIANT AND INDEX FOR OPERATORS ON THE REAL LINE PERIODIC AT INFINITY ⋮ Discrete Laplacian in a half‐space with a periodic surface potential I: Resolvent expansions, scattering matrix, and wave operators ⋮ Explicit formula for Schrödinger wave operators on the half-line for potentials up to optimal decay

Cites Work

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• \(C^*\)-algebras of operators on a half-space. II: Index theory
• \(C^*\)-algebras of almost periodic pseudo-differential operators
• Levinson's theorem for Schrödinger operators with point interaction: a topological approach
• Levinson’s Theorem: An Index Theorem in Scattering Theory
• Does Levinson’s theorem count complex eigenvalues?

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