We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Given a homogeneous elliptic partial differential operator 
$L$ with constant complex coefficients and a class of functions (jet-distributions) which are defined on a (relatively) closed subset of a domain 
$\Omega$ in 
${{\mathbf{R}}^{n}}$ and which belong locally to a Banach space 
$V$, we consider the problem of approximating in the norm of $V$ the functions in this class by “analytic” and “meromorphic” solutions of the equation 
$Lu\,=\,0$. We establish new Roth, Arakelyan (including tangential) and Carleman type theorems for a large class of Banach spaces $V$ and operators $L$. Important applications to boundary value problems of solutions of homogeneous elliptic partial differential equations are obtained, including the solution of a generalized Dirichlet problem.
