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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Representation of weakly additive operators
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by R. A. Decarlo and R. Saeks PDF
Proc. Amer. Math. Soc. 59 (1976), 55-61 Request permission

Abstract:

This paper characterizes a class of nonlinear operators termed “weakly additive". A distributional kernel representation is constructed. A counterexample to a conjecture by Gersho is then given via the distributional kernel formulation.
References
    A. Gersho, Nonlinear systems with a restricted additivity property, IEEE Trans. Circuit Theory 16 (1969), 150-154.
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  • L. Winslow and R. Saeks, Lossless nonlinear networks, IEEE Trans. Circuit Theory CT-19 (1972), 392. MR 381881
    • R. M. DeSantis, Causality structure of engineering systems, Ph. D. Thesis, Univ. of Michigan, Ann Arbor, Mich., 1971. R. DeCarlo, A distributional characterization of a weakly additive system, M. S. Thesis, Univ. of Notre Dame, Notre Dame, Ind., 1973. A. Gersho, Private communication.
  • A. H. Zemanian, Distribution theory and transform analysis. An introduction to generalized functions, with applications, McGraw-Hill Book Co., New York-Toronto-London-Sydney, 1965. MR 0177293
  • Michael Spivak, Calculus on manifolds. A modern approach to classical theorems of advanced calculus, W. A. Benjamin, Inc., New York-Amsterdam, 1965. MR 0209411
    • R. Median, Generalized impulse representation for time-varying networks, IEEE Trans. Circuit Theory 19 (1972), 106-107.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 55-61
  • MSC: Primary 47H99
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0412917-9
  • MathSciNet review: 0412917