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).

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).

##### MSC:

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 |

##### Keywords:

regularized trace; model problems; perturbed problem; ordinary differential operators; singular operators; partial differential operators
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\textit{V. A. Lyubishkin} and \textit{V. E. Podol'skij}, Math. Notes 54, No. 2, 790--793 (1993; Zbl 0878.47034); translation from Mat. Zametki 54, No. 2, 33--38 (1993)

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##### References:

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