On Compactness of Regular Integral Operators in the Space L1
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In this paper we obtain a sufficient condition for quite continuity of Fredholm type integral operators in the space L1(a, b). Uniform approximations by operators with degenerate kernels of horizontally striped structures are constructed. A quantitative error estimate is obtained. We point out the possibility of application of the obtained results to second kind integral equations, including convolution equations on a finite interval, equations with polar kernels, one-dimensional equations with potential type kernels, and some transport equations in non-homogeneous layers.
KeywordsCompactness of integral operator in the space of summable functions error estimate potential type kernel convolution equation transport equation
MSC2010 numbers45A05 45H05 45D05
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