On the approximation of isolated eigenvalues of ordinary differential operators. (English) Zbl 1156.34076
The main result of this article (Theorem 2) extends a result of Stolz and Weidmann (Theorem 1) on the approximation of isolated eigenvalues of singular Sturm-Liouville and Dirac operators by the eigenvalues of regular operators.
The definitions of two of the symbols appearing in Formula (4), namely \(\tau_n\) and \(W_a(u, f)\) are not given explicitly. We believe that \(\tau_n\) denotes the differential expression \(\tau\) restricted to the interval \((a_n, b_n)\), while \(W_a(u, f)\) denotes the value of the Wronskian of the functions \(u\) and \(f\) at \(a\).
The definitions of two of the symbols appearing in Formula (4), namely \(\tau_n\) and \(W_a(u, f)\) are not given explicitly. We believe that \(\tau_n\) denotes the differential expression \(\tau\) restricted to the interval \((a_n, b_n)\), while \(W_a(u, f)\) denotes the value of the Wronskian of the functions \(u\) and \(f\) at \(a\).
Reviewer: Vassilis G. Papanicolaou (Athena)
MSC:
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 34L16 | Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators |
| 34B20 | Weyl theory and its generalizations for ordinary differential equations |
References:
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