Threshold Effects near the Lower Edge of the Spectrum for Periodic Differential Operators of Mathematical Physics

@inproceedings{Birman2001ThresholdEN,
title={Threshold Effects near the Lower Edge of the Spectrum for Periodic Differential Operators of Mathematical Physics},
author={Michael V Birman and Tatyana Suslina},
year={2001}
}

In L2(R), we consider vector periodic DO A admitting a factorization A = X ∗X , where X is a homogeneous DO of first order. Many operators of mathematical physics have this form. The effects that depend only on a rough behavior of the spectral decomposition of A in a small neighborhood of zero are called threshold effects at λ = 0. An example of a threshold effect is the behavior of a DO in the small period limit. Another example is related to the negative discrete spectrum of the operator A−αV… CONTINUE READING

A. Laptev and T. A. Suslina, Discrete spectrum of the two-dimensional periodic elliptic second order operator perturbed by a decaying potential. I. Semibounded gap, (Russian), Algebra i Analiz, 12 (2000), no. 4, 36-78; English transl.: St. Petersburg Math. J., 12 • 2001

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