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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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Converse theorems and extensions in Chebyshev rational approximation to certain entire functions in $[\ast \ast \ast w(\ast \ast 0, +\infty )\ast \ast \ast w\ast \ast$
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by G. Meinardus, A. R. Reddy, G. D. Taylor and R. S. Varga PDF
Trans. Amer. Math. Soc. 170 (1972), 171-185 Request permission

Addendum: Trans. Amer. Math. Soc. 186 (1973), 499-502.

Abstract:

Recent interest in rational approximations to ${e^{ - x}}$ in $[0, + \infty )$, arising naturally in numerical methods for approximating solutions of heat-conduction-type parabolic differential equations, has generated results showing that the best Chebyshev rational approximations to ${e^{ - x}}$, and to reciprocals of certain entire functions, have errors for the interval $[0, + \infty )$ which converge geometrically to zero. We present here some related converse results in the spirit of the work of S. N. Bernstein.
References
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 170 (1972), 171-185
  • MSC: Primary 41A20; Secondary 26A93
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0310505-7
  • MathSciNet review: 0310505