ELASTODYNAMICAL SCATTERING BY N PARALLEL HALF-PLANES IN R(3)

Linear boundary value problems of elasticity describe the propagation of time- harmonic waves outside of N parallel half-plane shaped cracks in the Euclidian 3-space. Equivalent systems involving 6N Wiener-Hopf equations are obtained for first, second and third kind conditions si multaneously. To find explicit solutions, complex-valued matrix functi ons with nonrational entries, are to be factorized in a generalized ma nner. This is done for two double-knife screen crack problems in Part II. Problems for waves in acoustics, hydro-and electrodynamics with an analogous geometry for rigid walls, or perfectly conducting metallic sheets, are contained in the problems formulated above: In Part II, fo r pure Dirichlet-, or Neumann conditions, the corresponding (reduced) Wiener-Hopf operator is seen to be invertible by an operator Neumann s eries for all distances (not equal 0) between the N half-planes Sigma( m).