@Article{Castro2006,
author = "Castro, Luís P. and Natroshvili, David",
title = "The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces",
journal = "Opuscula Math.",
year = "2006",
volume = "26",
number = "2",
pages = "289--303",
doi = "http://dx.doi.org/10.7494/OpMath.2006.26.2.289",
url = "http://dx.doi.org/10.7494/OpMath.2006.26.2.289",
abstract = "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).",
keywords = "Helmholtz equation, boundary-transmission problem, wave diffraction, convolution type operator, Wiener-Hopf operator, Fredholm property, factorization",
issn = "1232-9274"
}