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On the summability of regularized traces of differential operators. (English. Russian original) Zbl 0878.47034
Math. Notes 54, No. 2, 790-793 (1993); translation from Mat. Zametki 54, No. 2, 33-38 (1993).
A regularized trace in the modern interpretation is expressed by a formula of form \[ \mathop{{\sum}'}_n(\mu_n- \lambda_n-{\mathcal A}(\lambda_n))={\mathcal B},\tag{2} \] where \(\mu_n\) and \(\lambda_n\) are the roots of the perturbed and model problems, \({\mathcal A}(\cdot)\), \(\mathcal B\) are expressions calculated explicitly by the parameters of the perturbed problem, and the prime in the summation sign denotes some summation method.
The aim of the present paper is to explain general methods that are common both for ordinary differential operators, singular operators, and partial differential operators, for the proof of formulae (2).

47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
58J05 Elliptic equations on manifolds, general theory
47G10 Integral operators
Full Text: DOI
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