A generalized collectively compact operator theory with an application to integral equations on unbounded domainsChandler-Wilde, S. N. and Zhang, B. (2002) A generalized collectively compact operator theory with an application to integral equations on unbounded domains. Journal of Integral Equations and Applications, 14 (1). pp. 11-52. ISSN 1938-2626
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1216/jiea/1031315433 Abstract/SummaryIn this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels
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