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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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A representation theorem and approximation operators arising from inequalities involving differential operators
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by D. Leviatan PDF
Trans. Amer. Math. Soc. 168 (1972), 85-99 Request permission

Abstract:

A representation of functions as integrals of a kernel $\psi (t;x)$, which was introduced by Studden, with respect to functions of bounded variation in $[0,\infty )$ is obtained whenever the functions satisfy some conditions involving the differential operators $(d/dt)\{ f(t)/{w_i}(t)\} ,i = 0,1,2, \ldots$. The results are related to the concepts of generalized completely monotonic functions and generalized absolutely monotonic functions in $(0,\infty )$. Some approximation operators for the approximation of continuous functions in $[0,\infty )$ arise naturally and are introduced; some sequence-to-function summability methods are also introduced.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 168 (1972), 85-99
  • MSC: Primary 41A35
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0296573-X
  • MathSciNet review: 0296573