On the spectrum of periodic elliptic operators

DOI10.1017/S0027763000004049zbMath0759.35016WikidataQ126125963 ScholiaQ126125963MaRDI QIDQ4029172

Jochen Brüning, Toshikazu Sunada

Publication date: 7 March 1993

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

selfadjoint operatorsband structurecomplete Riemannian manifoldsymmetric elliptic operatordiscontinuous isometric action of a groupKadison property

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Schrödinger operator, Schrödinger equation (35J10) Linear operators in (C^*)- or von Neumann algebras (47C15)

Related Items (13)

Green's function asymptotics of periodic elliptic operators on abelian coverings of compact manifolds ⋮ Noncommutative Bloch analysis of Bochner Laplacians with nonvanishing gauge fields ⋮ EXISTENCE OF SPECTRAL GAPS, COVERING MANIFOLDS AND RESIDUALLY FINITE GROUPS ⋮ Good Wannier bases in Hilbert modules associated to topological insulators ⋮ Generalized Bloch analysis and propagators on Riemannian manifolds with a discrete symmetry ⋮ Index type invariants for twisted signature complexes and homotopy invariance ⋮ Burghelea-Haller analytic torsion of $\mathbb {Z}_{2}$-graded elliptic complexes ⋮ Spectral properties of the periodic magnetic Schrödinger operator in the high-energy region. Two-dimensional case ⋮ Noncommutative Bloch theory ⋮ Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds ⋮ An overview of periodic elliptic operators ⋮ Exponentially localized Wannier functions in periodic zero flux magnetic fields ⋮ Periodic manifolds with spectral gaps

Cites Work

• Unnamed Item
• Trace formula for Hill's operators
• KK-groups of crossed products by groups acting on trees
• Unitary representations of fundamental groups and the spectrum of twisted Laplacians
• An asymptotic expansion for the heat equation
• On L²-Betti Numbers for Abelian Groups
• Group C*-Algebras and the Spectrum of a Periodic Schrödinger Operator on a Manifold

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