Question about existence of function with given derivatives - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T17:18:28Z http://mathoverflow.net/feeds/question/109131 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109131/question-about-existence-of-function-with-given-derivatives Question about existence of function with given derivatives user 12345 2012-10-08T10:17:55Z 2012-10-22T19:22:01Z <p>Let $f_n : U \rightarrow \mathbb R$ be a given sequence of functions of class $C^\infty$ on open subsets $U \subset \mathbb R^n$. Does there exist a function $F:\mathbb R \times U \rightarrow \mathbb R$ of class $C^\infty$ such that $$\frac{\partial^n f}{\partial t^n}(0, x)=f_n(x)$$ for $n=0,1,2,\ldots$ and all $x \in U ?$ </p> http://mathoverflow.net/questions/109131/question-about-existence-of-function-with-given-derivatives/109148#109148 Answer by Alexandre Eremenko for Question about existence of function with given derivatives Alexandre Eremenko 2012-10-08T13:11:32Z 2012-10-08T18:45:25Z <p>This is Theorem 1.2.6 in L. Hormander, Analysis of linear partial differential operators, vol. I.</p>