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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 1973 Volume 14, Issue 6, Pages 843–852 (Mi mzm7303)

The distribution of eigenvalues of the Dirac operator

M. Otelbaev

Moscow State University

Abstract: The Dirac system is studied on $(-\infty, \infty)$. Asymptotic formulas are obtained of the distribution for both positive, and negative eigenvalues. The asymptotic formulas, established in Theorem 1, are essentially different from formulas obtained by Sargsyan [1], and permit asymptotic formulas to be written for the distribution of positive (negative) eigenvalues, even in those cases when the negative (positive) spectrum is continuous, if appropriate conditions hold on the potential.

UDC: 517.9

Received: 25.03.1972


 English version:
Mathematical Notes, 1973, 14:6, 1043–1048

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