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Asymptote of the eigenvalues of a completely continuous operator

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Abstract

It is proved that ifϕ(x) is the majorant of the s-numbers of a completely continuous operator A (i.e.,ϕ∼'(x)≲- 0, Sn(A) ≤ϕ(n)) and if there are found numbersρ ε [0, 1] and r0 > 0 such that r0 ϕ′ (r)/ϕ(r) will be monotonic in (r0,∞), then for someα > 0,ϕ((αx) will be a majorant of the eigenvalues of A.

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Literature cited

  1. I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Nonself-Adjoint Operators [in Russian], Moscow (1965).

  2. B. Ya. Levin, Distribution of the Roots of Entire Functions [in Russian], Moscow (1956).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    K. Kh. Boimatov

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  1. K. Kh. Boimatov
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Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 487–492, October, 1973.

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Boimatov, K.K. Asymptote of the eigenvalues of a completely continuous operator. Mathematical Notes of the Academy of Sciences of the USSR 14, 837–839 (1973). https://doi.org/10.1007/BF01108808

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  • DOI: https://doi.org/10.1007/BF01108808

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