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Some spectral relations

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Abstract

We consider the zeta function of a second-order differential operator which has a secon-dorder turning point:

$$Lu = \frac{{d^2 u}}{{dx^2 }} + [\lambda ^2 q(x) + R(x)]u,$$

where q(x)=x2q1(x), q1(x)≠0 and u (0)=u (1)=0. We construct an asymptotic series and calculate regularized traces for the eigenvalues of this operator.

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Literature cited

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Authors and Affiliations

  1. Moscow State University, USSR

    A. A. Stakun

Authors
  1. A. A. Stakun
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Additional information

Translated from Matematicheskie Zametki, Vol. 18, No. 4, pp. 561–568, October, 1975.

The author thanks V. A. Sadovnichii for his constant attention to this work.

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Stakun, A.A. Some spectral relations. Mathematical Notes of the Academy of Sciences of the USSR 18, 923–927 (1975). https://doi.org/10.1007/BF01153045

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  • DOI: https://doi.org/10.1007/BF01153045

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