Fredholm determinant is a generalization of a determinant of a finite-dimensional matrix to a class of operators on Banach spaces which differ from identity by a trace class operator or by an appropriate analogue in more abstract context (there are appropriate determinants on certain Banach ideals). It is often considered as an analytic function of a perturbation parameter . The calculations with Fredholm determinants have applications in operator theory, random matrix theory, integrable models etc.
In his original setup, Fredholm attached the determinant
to the Fredholm integral equation of the second kind
and is an entire function of such that iff the integral equation has a unique solution.
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Physics applications
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