The two-point time and temperature dependent correlation functions for the XX0 one-dimensional model in constant magnetic field are represented (in the thermodynamical limit) as Fredholm determinants of linear integral operators.

We describe the generic behavior of Fredholm indices in the space of Toeplitz operators. We relate this behavior to certain conjectures and open problems that arise in the context of the Quantum Hall Effect.

We provide sufficient conditions for vector-valued Fredholm integral operators and their commonly used spatial discretizations to be positive in terms of an order relation induced by a corresponding cone. It turns out that reasonable Nyström methods preserve positivity. Among the projection methods, persistence is obtained simplest ones based on polynomial, piecewise linear or specific cubic in...

Fredholm determinant asymptotics of convolution operators on large finite intervals with rational symbols having real zeros are studied. The explicit asymptotic formulae obtained can be considered as a direct extension of the Ahiezer-Kac formula to symbols with real zeros.

A general integral formula for the spectral flow of a path of unbounded selfadjoint Fredholm operators subject to certain summability conditions is derived from the interpretation of the spectral flow as a winding number.

The invertible, compact and Fredholm multiplication operators on generalized Lorentz-Zygmund (GLZ) spaces Lp,q;α, 1 < p ≤ ∞, 1 ≤ q ≤ ∞, α in the Euclidean space R, are characterized in this paper.