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Proceedings of the American Mathematical Society

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

 

 

On inequalities for differential operators


Author: Richard Bellman
Journal: Proc. Amer. Math. Soc. 9 (1958), 589-597
MSC: Primary 26.00
DOI: https://doi.org/10.1090/S0002-9939-1958-0110771-5
MathSciNet review: 0110771
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Abstract: In this paper we study the following problem: Given that certain functionals of $ u$ and its derivatives belong to given $ {\text{L}}$classes over the infinite interval, what can be said about the $ {\text{L}}$-classes of other functionals? Utilizing a simple device from the theory of linear differential equations, we obtain a number of results due to Landau, Kolmogoroff, Halperin-von Neumann, and Nagy, together with some extensions.


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DOI: https://doi.org/10.1090/S0002-9939-1958-0110771-5
Article copyright: © Copyright 1958 American Mathematical Society