%0 Journal Article %T The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces %A Lu¨ªs P. Castro %A David Natroshvili %J Opuscula Mathematica %D 2006 %I AGH University of Science and Technology %X We consider a boundary-transmission problem for the Helmholtz equation, in a Bessel potential space setting, which arises within the context of wave diffraction theory. The boundary under consideration consists of a strip, and certain reactance conditions are assumed on it. Operator theoretical methods are used to deal with the problem and, as a consequence, several convolution type operators are constructed and associated to the problem. At the end, the well-posedness of the problem is shown for a range of regularity orders of the Bessel potential spaces, and for a set of possible reactance numbers (dependent on the wave number). %K Helmholtz equation %K boundary-transmission problem %K wave diffraction %K convolution type operator %K %K Wiener¨CHopf operator %K Fredholm property %K factorization %U http://www.opuscula.agh.edu.pl/vol26/2/art/opuscula_math_2620.pdf