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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.

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