Article
Ufa Mathematical Journal
Volume 7, Number 1, pp. 70-82
General regularized trace formulae for loaded equations
Tsopanov I.D.
DOI:10.13108/2015-7-1-70
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We consider regularized traces for differential operators with the coefficients at the powers of a spectral parameter being the values of an unknown function at prescribed points in its domain. Such differential operators are interpreted as polynomial operator pencils whose coefficients are unbounded fininte-dimensional operators. Basing on the theory of M.V. Keldysh, we construct general regularized trace formulae for such operator pencils. The obtained formulae develop a known result by V.A. Sadovnichii and V.A. Lyubishkin for relative finite-dimensional perturbations of self-adjoint operators.