Perturbations of limit-circle expressions
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- by Thomas T. Read PDF
- Proc. Amer. Math. Soc. 56 (1976), 108-110 Request permission
Abstract:
It is shown that for any limit-circle expression $L(y) = \Sigma _{j = 0}^n {{p_j}{y^{(j)}}}$, any sequence of disjoint intervals $\{ [{a_k},{b_k}]\} _{k = 1}^\infty$ such that ${a_k} \to \infty$ as $k \to \infty$, and any $i \leqslant n - 1$, there is an expression $M(y) = \Sigma _{j = 0}^n {{q_j}{y^{(j)}}}$ such that ${q_i} = {p_i}$ except on $\cup ({a_k},{b_k}),{q_j} = {p_j}$ for all $j \ne i$, and such that $M$ is not limit-circle.References
- M. S. P. Eastham and M. L. Thompson, On the limit-point, limit-circle classification of second-order ordinary differential equations, Quart. J. Math. Oxford Ser. (2) 24 (1973), 531–535. MR 417481, DOI 10.1093/qmath/24.1.531
- R. S. Ismagilov, On the self-adjointness of the Sturm-Liouville operator, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 161–166 (Russian). MR 0155037
- Ian Knowles, Note on a limit-point criterion, Proc. Amer. Math. Soc. 41 (1973), 117–119. MR 320425, DOI 10.1090/S0002-9939-1973-0320425-6
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 108-110
- DOI: https://doi.org/10.1090/S0002-9939-1976-0399560-5
- MathSciNet review: 0399560