Regularized Determinants of Self-Adjoint OperatorsOberseminar Global Analysis and Operator Algebras

by Luiz Hartmann (Federal University of Sao Carlos)

Tuesday Jul 7, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Lipschitzsaal (Mathezentrum)

Given an invertible self-adjoint operator $L$ in a Hilbert space, under a discrete dimension spectrum assumption on $L$, I will describe the relation between the (regularized) Fredholm determinant, $\det_p(I+z\cdot L^{-1})$, and the zeta regularized determinant, $\det_\zeta(L+z)$. Moreover, I will discuss the asymptotic expansion of the Fredholm determinant in relation to the heat trace coefficients, showing that the constant term equals $-\log\det_\zeta(L)$.