Extended Kac-Akhiezer formulae and the Fredholm determinant of finite section Hilbert-Schmidt kernels

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This paper deals with some results (known as Kac-Akhiezer formulae) on generalized Fredholm determinants for Hilbert-Schmidt operators onL 2-spaces, available in the literature for convolution kernels on intervals. The Kac-Akhiezer formulae have been obtained for kernels, which are not necessarily of convolution nature and for domains in ℝ n .