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Transactions of the American Mathematical Society

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

 

 

Inclusion relations between power methods and matrix methods of limitation


Author: Abraham Ziv
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1977-0481712-2
Article copyright: © Copyright 1977 American Mathematical Society