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|Title:||Definable continuous solutions of linear equations|
|Abstract:||In this paper, we study a generalization of a question, raised by C. Fefferman and J. Kollár, on the existence of solutions of linear functional equations. Suppose that R is a definably complete expansion of a real closed field.RI C; /. Let f; g1;:::; gkW Rn ! R be continuous functions that are definable in R. We prove that if there exist continuous functions y1;:::; ykW Rn ! R such that f D g1y1 C C gkyk, then there exist continuous functions y1;:::; yk such that y1;:::; yk are definable in R and f D g1y1 C C gkyk.|
|Appears in Collections:||CMUL: Journal Articles|
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