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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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Inclusion relations between power methods and matrix methods of limitation
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by Abraham Ziv PDF
Trans. Amer. Math. Soc. 234 (1977), 185-211 Request permission

Abstract:

A matrix method of limitation is a generalization of both ordinary Toeplitz methods and semicontinuous methods. A power method is a generalization of both Abel’s method and Borel’s exponential method. The main concern of this paper is to find necessary and sufficient conditions for the field of a given power method to be included in the field of a given matrix method. The problem is solved for a wide family of power methods which includes all Abel type methods, the logarithmic method, all Borel type methods and others (also nonregular power methods). Preliminary results, which serve as tools in the solution of the main problem, clarify some aspects of the nature of the field of a power method as an FK space.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 234 (1977), 185-211
  • MSC: Primary 40C15; Secondary 40D25
  • DOI: https://doi.org/10.1090/S0002-9947-1977-0481712-2
  • MathSciNet review: 0481712