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# Perturbations of Limit-Circle Expressions

Proceedings of the American Mathematical Society
Vol. 56, No. 1 (Apr., 1976), pp. 108-110
DOI: 10.2307/2041585
Stable URL: http://www.jstor.org/stable/2041585
Page Count: 3
It is shown that for any limit-circle expression $L(y) = \Sigma^n_{j = 0} p_jy^{(j)}$, any sequence of disjoint intervals $\{\lbrack a_k, b_k \rbrack\}^\infty_{k = 1}$ such that $a_k \rightarrow \infty$ as $k \rightarrow \infty$, and any $i \leq n - 1$, there is an expression $M(y) = \Sigma^n_{j = 0} q_jy^{(j)}$ such that $q_i = p_i$ except on $\cup(a_k, b_k), q_j = p_j$ for all $j \neq i$, and such that $M$ is not limit-circle.