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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Perturbations of limit-circle expressions


Author: Thomas T. Read
Journal: Proc. Amer. Math. Soc. 56 (1976), 108-110
DOI: https://doi.org/10.1090/S0002-9939-1976-0399560-5
MathSciNet review: 0399560
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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.


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Keywords: <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$n$">th order ordinary differential expression, Weyl theory, limit-circle condition
Article copyright: © Copyright 1976 American Mathematical Society