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Proceedings of the American Mathematical Society

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

 

 

Interpolating functions associated with second-order differential equations


Author: William F. Trench
Journal: Proc. Amer. Math. Soc. 78 (1980), 253-258
MSC: Primary 34C10; Secondary 33A40, 34B25
DOI: https://doi.org/10.1090/S0002-9939-1980-0550507-9
MathSciNet review: 550507
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Abstract: Functions are exhibited which interpolate the magnitude of a solution y of a linear, homogeneous, second-order differential equation at its critical points, $ \vert y'\vert$ at the zeros of y, and $ \vert\smallint _{{x_0}}^xy(t)h(t)\;dt\vert$ at the zeros of y. Except for a normalization condition, the interpolating functions are independent of the specific solution y. A theorem similar in its conclusions to the Sonin-Pólya-Butlewski theorem is presented and examples are given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0550507-9
Keywords: Zeros, interpolation, cylinder function, Sonin-Pólya-Butlewski theorem
Article copyright: © Copyright 1980 American Mathematical Society