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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Selfadjoint nonoscillatory second order linear $B^ \ast$-algebra differential equations
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by Manuel Lopez PDF
Proc. Amer. Math. Soc. 97 (1986), 71-74 Request permission

Abstract:

The main result in this paper states that the second order linear ${B^*}$-algebra differential equation $(p(t)y’) + q(t)y = 0$, where $p(t)$ is positive and $q(t)$ is Hermitian for each $t$, is nonoscillatory on $[{t_0},\infty )$ if the scalar equation $({\left \| {{p^{ - 1}}(t)} \right \|^{ - 1}}W’)’ + \left \| {q(t)} \right \|W = 0$ is nonoscillatory on $[{t_0},\infty )$. Consequently, every criterion on nonoscillation in the scalar case automatically produces another one in the ${B^*}$-algebra case.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 97 (1986), 71-74
  • MSC: Primary 34G10; Secondary 34C10, 46K99
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0831390-6
  • MathSciNet review: 831390