On Some Functional Equations and Representations of Topological Semigroups |
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Authors: | E V Shulman |
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Institution: | (1) School of Mathematical Sciences, Tel-Aviv University, Israel |
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Abstract: | Let a representation T of a semigroup G on a linear space X be given. We call x ∈ X a finite vector if its orbit T(G) is contained in a finite-dimensional subspace. In this paper, some statements about finite vectors are applied to the following problem. For a given positive integer n > 1, describe all continuous functions f : G → ? such that the function (x1,..., x n ) ? f(x1 + ? + x n ) can be polynomially expressed via functions of sums of fewer variables. |
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Keywords: | functional equation on a semigroup addition theorem representation of a topological semigroup |
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