Far Eastern Mathematical Journal

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Some properties of the resolvent kernels for integral equations with bi-Carleman kernels


Igor M. Novitskii

2016, issue 2, Ñ. 186-208


Abstract
We prove that, at regular values lying in a region of generalized strong convergence, the resolvent kernels corresponding to a continuous bi-Carleman kernel vanishing at infinity can be expressed as uniform limits of sequences of resolvent kernels associated with its approximating Hilbert-Schmidt-type subkernels.

Keywords:
linear integral equation of the second kind, bounded integral linear operator, Fredholm resolvent, resolvent kernel, bi-Carleman kernel, Hilbert-Schmidt kernel, nuclear operator, regular value, characteristic set

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References

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