Statement
Suppose U is an open set in the Euclidean space Rn, and suppose that f0, f1 ... is a sequence of smooth, complex-valued functions on U. If I is an any open interval in R containing 0 (possibly I = R), then there exists a complex-valued smooth function F(t, x) defined on I×U, such that
for k ≥ 0 and x in U.
Read more about this topic: Borel's Lemma
Famous quotes containing the word statement:
“Most personal correspondence of today consists of letters the first half of which are given over to an indexed statement of why the writer hasn’t written before, followed by one paragraph of small talk, with the remainder devoted to reasons why it is imperative that the letter be brought to a close.”
—Robert Benchley (1889–1945)
“It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.”
—John Dewey (1859–1952)
“No statement about God is simply, literally true. God is far more than can be measured, described, defined in ordinary language, or pinned down to any particular happening.”
—David Jenkins (b. 1925)