Article

Proceedings of the Indian Academy of Sciences - Mathematical Sciences

, Volume 104, Issue 3, pp 581-591

First online:

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

  • S Ganapathi RamanAffiliated withDepartment of Mathematics, Indian Institute of Sciences
  • , R Vittal RaoAffiliated withDepartment of Mathematics, Indian Institute of Sciences

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Abstract

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 .

Keywords

Hilbert-Schmidt integral operator Fredholm determinant Kac-Akhiezer formula