# Nahum Zobin
College of William and Mary

## Smooth functions in bad domains and Fourier analysis in Fock space

Let $\Omega $ be a bounded connected open subset of $R^n$.
Consider the space $W^{k+1}_\infty (\Omega)$ of functions with
partial derivatives of order $k+1$ bounded in $\Omega.$
Are these functions extendible to the functions of the same class
in the whole $R^n$? In 1934 H. Whitney proposed a geometric
condition on $\Omega$ (equivalence of the geodesic distance in
$\Omega $ to the Euclidean distance) which implies such
extendability. A long standing
question was if this condition is also necessary. We introduce
techniques ( a kind of Fourier analysis in the Fock spaces) which
allowed to give a very complete answer to this question.