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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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Interpolating functions associated with second-order differential equations
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by William F. Trench PDF
Proc. Amer. Math. Soc. 78 (1980), 253-258 Request permission

Abstract:

Functions are exhibited which interpolate the magnitude of a solution y of a linear, homogeneous, second-order differential equation at its critical points, $|y’|$ at the zeros of y, and $|\smallint _{{x_0}}^xy(t)h(t)\;dt|$ 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
  • © Copyright 1980 American Mathematical Society
  • 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