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A characterization of generalized exponential polynomials in terms of decomposable functions

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 نشر من قبل Miklos Laczkovich
 تاريخ النشر 2018
  مجال البحث
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 تأليف Miklos Laczkovich




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Let $G$ be a topological commutative semigroup with unit. We prove that a continuous function $fcolon Gto cc$ is a generalized exponential polynomial if and only if there is an $nge 2$ such that $f(x_1 +ldots +x_n )$ is decomposable; that is, if $f(x_1 +ldots +x_n )=sumik u_i cd v_i$, where the function $u_i$ only depends on the variables belonging to a set $emp e E_i subsetneq { x_1 stb x_n }$, and $v_i$ only depends on the variables belonging to ${ x_1 stb x_n } se E_i$ $(i=1stb k)$.



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