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Regularized traces of higher-order singular differential operators. (English) Zbl 1159.34354
Math. Notes 83, No. 1, 37-47 (2008); translation from Mat. Zametki 83, No. 1, 39-49 (2008).
Summary: We consider singular differential operators of order \(2m,m \in \mathbb N\), with discrete spectrum in \(L_2[0,+\infty)\). For self-adjoint extensions given by the boundary conditions \(y(0) = y''(0) = \cdots = y^{(2m - 2)}(0) = 0\) or \(y'(0) = y'''(0) = \cdots = y^{(2m - 1)}(0) = 0\), we obtain regularized traces. We present the explicit form of the spectral function, which can be used for calculating regularized traces.

34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
47E05 General theory of ordinary differential operators
Full Text: DOI
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