The Ultimate Borel's lemma - American History Information Guide and Reference

In mathematics, Borel's lemma is an important result about partial differential equations named after Émile Borel.

Suppose $U$ is an open set in the Euclidean space Rⁿ, and suppose that $f 0, f 1,...$ is a sequence of smooth, complex-valued functions on $U$ . Then there exists a smooth function $F = F (t, x)$ defined on R× $U$ with complex values, such that

$\left(\frac{\partial^k}{\partial t^k}F\right)(0,x) = f_k(x),$

for all $k = 0,1,...$ , and $x$ in $U .$

A constructive proof of this result is given in Golubitsky (1974).

References

M. Golubitsky, V. Guillemin (1974). Stable mappings and their singularities. Springer-Verlag, Graduate texts in Mathematics: Vol. 14. ISBN 0387900721.

Categories: Partial differential equations

Last updated: 05-21-2005 19:48:24

Your American History Reference Guide! - Borel's lemma

Borel's lemma

References

Your American History Reference Guide!
- Borel's lemma