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2003-2004 Dilatations of graphs and Taylor's formula: some results about convergence.
Silvano Delladio
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Real Anal. Exchange 29(2): 687-713 (2003-2004).


The graph of a function $f$ is subjected to non-homogeneous dilatations around the point $(x_0;f(x_0))$, related to the Taylor's expansion of $f$ at $x_0$. Some questions about convergence are considered. In particular the dilated images of the graph are proved to behave nicely with respect to a certain varifold-like convergence. Further and stronger results are shown to hold in such a context, by suitably reinforcing the assumptions.


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Silvano Delladio. "Dilatations of graphs and Taylor's formula: some results about convergence.." Real Anal. Exchange 29 (2) 687 - 713, 2003-2004.


Published: 2003-2004
First available in Project Euclid: 7 June 2006

zbMATH: 1071.28005
MathSciNet: MR2083806

Primary: 41A10 , 49Q15 , 53A05 , 54G20
Secondary: 28A33 , 28A75 , 28A78 , 54C20

Keywords: Convergence of functions , Convergence of surfaces , counterexamples , geometric measure theory , Non-homogeneous blow-ups , Taylor polynomials

Rights: Copyright © 2003 Michigan State University Press

Vol.29 • No. 2 • 2003-2004
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