On the structure of band edges of 2d periodic elliptic operators

Zaidenberg M., Krein S., Kuchment P, Pankov A., Banach bundles and linear operators

Original

1975

Earlier work this paper cites.

Ashcroft N., Mermin N., Solid State Physics

1976

Earlier work this paper cites.

Reed M., Simon B., Methods of Modern Mathematical Physics, Volume IV: Analysis of Operators

1978

Earlier work this paper cites.

Kirsh W., Simon B., Comparison theorems for the gap of Schrödinger operators

1987

Earlier work this paper cites.

Colin de Verdiere Y., Sur les singularités de Van Hove génériques

1991

Earlier work this paper cites.

Kuchment P., Floquet theory for Partial Differential Equations

1993

Earlier work this paper cites.

Kato T., Perturbation Theory for Linear Operators

1995

Earlier work this paper cites.

Birman M. Sh., Suslina T. A., The two-dimensional periodic magnetic Hamiltonian is absolutely continuous

1998

Earlier work this paper cites.

Birman M. Sh., Suslina T. A., Absolute continuity of a two-dimensional periodic magnetic Hamiltonian with discontinuous vector potential

1999

Earlier work this paper cites.

Birman M. Sh., Suslina T. A., Two-dimensional periodic Pauli operator. The effective masses at the lower edges of the spectrum

1999

Cited alongside, same era.

Birman M. Sh., Suslina T. A., A periodic magnetic Hamiltonian with a variable metric. The problem of absolute continuity

2000

Cited alongside, same era.

Klopp F., Ralston J., Endpoints of the spectrum of periodic operators are generically simple

2000

Cited alongside, same era.

Kuchment P., The mathematics of photonic crystals

2001

Cited alongside, same era.

Kuchment P., Levendorskii S., On the structure of spectra of periodic elliptic operators

2001

Cited alongside, same era.

Kuchment P., Pinchover Y., Integral representations and Liouville type theorems for solutions of periodic elliptic equations

Shterenberg R., An example of a periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum

2005

Later among the works it cites.

Shterenberg R., On the structure of the lower spectral edge for a magnetic Schrödinger operator with small magnetic potential

2006

Later among the works it cites.

Kuchment P., Pinchover Y., Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds

2007

Later among the works it cites.

Kuchment P., Raich A., Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case

2012

Later among the works it cites.

Hoang V., Radosz M., Absence of bound states for waveguides in 2D periodic structures

2014

Later among the works it cites.