ScalingStacks

Remark 4.12 . [04JC]

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Remark 4.12.

For any given formal power series in two variables h=∑hi​j​x1i​x2jh=\sum h_{ij}x_{1}^{i}x_{2}^{j} whose coefficients are smooth functions hi​j=hi​j​(r)h_{ij}=h_{ij}(r) on II, there is a function HH on D2×ID^{2}\times I whose germ along Δ\Delta is hh. An analogous statement in the case of a formal power series in one variable with real coefficients is standard (cf. [31] Exercise 13, page 384). It is an exercise to check that it is also true in two variables with coefficients depending on a parameter.

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