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Representation of weakly additive operators

Authors: R. A. Decarlo and R. Saeks
Journal: Proc. Amer. Math. Soc. 59 (1976), 55-61
MSC: Primary 47H99
MathSciNet review: 0412917
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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 [Enhancements On Off] (What's this?)

  • [1] A. Gersho, Nonlinear systems with a restricted additivity property, IEEE Trans. Circuit Theory 16 (1969), 150-154.
  • [2] L. A. Zadeh, A contribution to the theory of nonlinear systems, J. Franklin Inst. 255 (1953), 387–408. MR 0058452,
  • [3] L. Winslow and R. Saeks, Lossless nonlinear networks, IEEE Trans. Circuit Theory CT-19 (1972), 392. MR 0381881
  • [4] R. M. DeSantis, Causality structure of engineering systems, Ph. D. Thesis, Univ. of Michigan, Ann Arbor, Mich., 1971.
  • [5] R. DeCarlo, A distributional characterization of a weakly additive system, M. S. Thesis, Univ. of Notre Dame, Notre Dame, Ind., 1973.
  • [6] A. Gersho, Private communication.
  • [7] 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
  • [8] Michael Spivak, Calculus on manifolds. A modern approach to classical theorems of advanced calculus, W. A. Benjamin, Inc., New York-Amsterdam, 1965. MR 0209411
  • [9] R. Median, Generalized impulse representation for time-varying networks, IEEE Trans. Circuit Theory 19 (1972), 106-107.

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Keywords: Distribution, causal continuous translation invariant nonlinear operator, kernel, memoryless nonlinearity
Article copyright: © Copyright 1976 American Mathematical Society

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