Abstract
Whe shall study here generalized boundary-value problems (including potentials) for homogeneous elliptic systems of convolution equations in a half-space. The main result is Theorem 3, giving the necessary and sufficient conditions for a problem to be well-posed. Actually we establish an isomorphism between the space of unknowns and the data space. We use a pure L2-theory for systems of order 0. But we outline the way to obtain LP - theory and also the way to treat systems with various degrees of homogeneity - by introducing suitable Hs spaces for the various components. At the end we add several other remarks. More details will appear in [8], which is a natural continuation of [7].
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