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A generalized collectively compact operator theory with an application to integral equations on unbounded domains. (English) Zbl 1055.47017

The authors develop a generalization of collectively compact operator theory in Banach spaces. The main feature is that the operators involved are not required to be compact in the norm topology. Instead, it is assumed that the image of a bounded set under operator family is sequentially compact in a weak topology. The theory is applied to the investigation of systems of second order integral equations on unbounded domains. This class includes Wiener-Hopf integral equations with \(L^1\) convolution kernels.

MSC:

47B07 Linear operators defined by compactness properties
47A50 Equations and inequalities involving linear operators, with vector unknowns
46B50 Compactness in Banach (or normed) spaces
47N20 Applications of operator theory to differential and integral equations
45F15 Systems of singular linear integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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References:

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