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On the number of negative eigenvalues of a partial integral operator

Abstract

We find the lower boundary for the essential spectrum of a Fredholm type partial integral operator H. We also obtain an estimate for the number of eigenvalues below this boundary.

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Correspondence to Yu. Kh. Eshkabilov.

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Original Russian Text © Yu.Kh. Eshkabilov and R.R. Kucharov, 2014, published in Matematicheskie Trudy, 2014, Vol. 17, No. 1, pp. 128–144.

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Eshkabilov, Y.K., Kucharov, R.R. On the number of negative eigenvalues of a partial integral operator. Sib. Adv. Math. 25, 179–190 (2015). https://doi.org/10.3103/S1055134415030037

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Keywords

  • essential spectrum
  • discrete spectrum
  • the lower boundary of the essential spectrum
  • Fredholm type partial integral operator