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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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