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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The rank of a Hardy field
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by Maxwell Rosenlicht PDF
Trans. Amer. Math. Soc. 280 (1983), 659-671 Request permission

Abstract:

A Hardy field is a field of germs of real-valued functions on positive half-lines that is closed under differentiation. Its rank is the rank of the associated ordered abelian group, the value group of the canonical valuation of the field. The properties of this rank are worked out, its relevance to asymptotic expansions indicated, examples provided, and applications given to the order of growth of solutions of ordinary differential equations.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 280 (1983), 659-671
  • MSC: Primary 12D15; Secondary 12H05, 13N05, 26A12, 34E05, 41A60
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0716843-5
  • MathSciNet review: 716843