## Estimates of the discrete spectrum of a linear operator pencil.(English)Zbl 1117.47009

Author’s abstract: Based on the direct methods of the perturbation theory, sufficient conditions are established for the finiteness of the discrete spectrum of linear pencils of the form $$L(\lambda)=B-\lambda A$$, where $$A$$ and $$B$$ are bounded selfadjoint operators. An estimate for the discrete spectrum is also presented. As applications, we study the spectrum of the characteristic equation of radiation energy transfer.

### MSC:

 47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) 47A10 Spectrum, resolvent 47A55 Perturbation theory of linear operators 34L05 General spectral theory of ordinary differential operators 34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators 46J10 Banach algebras of continuous functions, function algebras 47N55 Applications of operator theory in statistical physics (MSC2000)
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