# Fr\'echet-valued formal power series

12 Jan 2019 Quang Thai Thuan

Let $A$ be a non-projectively-pluripolar set in a Fr\'{e}chet space $E.$ We give sufficient conditions to ensure the convergence on some zero-neighbourhood in $E$ of a (sequence of) formal power series of Fr\'{e}chet-valued continuous homogeneous polynomials provided that the convergence holds at a zero-neighbourhood of each complex line $\ell_a := \C a$ for every $a \in A.$..

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